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Profit and Loss

Reading Time: 180 mins

Solved Examples: 75

Practice Questions: 7

Solved Examples

Question 1: A shopkeeper buys an article for ¤800 and sells it for ¤950. Find the profit earned.

Cost Price (CP) = ¤800
Selling Price (SP) = ¤950
Since SP > CP, there is a profit.
Profit = SP − CP
= ¤950 − ¤800
= ¤150
Therefore, the profit earned is ¤150.

Question 2: A shopkeeper buys a chair for ¤2,400 and sells it for ¤2,100. Find the loss incurred.

Cost Price (CP) = ¤2,400
Selling Price (SP) = ¤2,100
Since CP > SP, there is a loss.
Loss = CP − SP
= ¤2,400 − ¤2,100
= ¤300
Therefore, the loss incurred is ¤300.

Question 3: An article is purchased for ¤1,200 and sold for ¤1,500. Find the profit percentage.

Cost Price (CP) = ¤1,200
Selling Price (SP) = ¤1,500
Profit = SP − CP
= ¤1,500 − ¤1,200
= ¤300
Profit % = (Profit ÷ CP) × 100
= (300 ÷ 1,200) × 100
= 25%
Therefore, the profit percentage is 25%.

Question 4: An article is bought for ¤2,000 and sold for ¤1,700. Find the loss percentage.

Cost Price (CP) = ¤2,000
Selling Price (SP) = ¤1,700
Loss = CP − SP
= ¤2,000 − ¤1,700
= ¤300
Loss % = (Loss ÷ CP) × 100
= (300 ÷ 2,000) × 100
= 15%
Therefore, the loss percentage is 15%.

Question 5: A shopkeeper buys an article for ¤1,500 and sells it at a profit of 20%. Find the selling price.

Cost Price (CP) = ¤1,500
Profit % = 20%
SP = CP × (100 + Profit %) ÷ 100
= 1,500 × (100 + 20) ÷ 100
= 1,500 × 120 ÷ 100
= ¤1,800
Therefore, the selling price of the article is ¤1,800.

Question 6: An article is sold for ¤2,400 at a profit of 20%. Find its cost price.

The SP is ¤120 when CP is ¤100
The SP is ¤ 1 when CP is ¤(100/120)
The SP is ¤2,400 when CP is ¤2,400x(100/120) = ¤2,000
So the cost price of the artile is ¤2,000

Question 7: A mobile phone is sold for ¤27,000 at a profit of 8%. Find the cost price.

Selling Price (SP) = ¤27,000
Profit % = 8%
CP = 27,000 × 100 ÷ 108
= ¤25,000
Therefore, the cost price of the mobile phone is ¤25,000.

Question 8: An article is sold for ¤1,800 at a loss of 10%. Find its cost price.

The article is sold at a loss of 10%.
When the SP is ¤90 the CP is ¤100
When the SP is ¤1 the CP is ¤(100/90)
When the SP is ¤1,800 the CP is ¤1,800x(100/90) = ¤2,000

Question 9: A trader sells a machine for ¤42,500 at a loss of 15%. Find the cost price of the machine.

Selling Price (SP) = ¤42,500
Loss % = 15%
CP = 42,500 × 100 ÷ (100 − 15)
= 42,500 × 100 ÷ 85
= ¤50,000
Therefore, the cost price of the machine is ¤50,000.

Question 10: A shirt has a marked price of ¤2,400. A discount of 15% is offered. Find the selling price.

Marked Price (MP) = ¤2,400
Discount = 15% of ¤2,400
= (15 ÷ 100) × 2,400
= ¤360
Selling Price (SP) = MP − Discount
= ¤2,400 − ¤360
= ¤2,040
Therefore, the selling price of the shirt is ¤2,040.

Alternate solution:
When MP is 100 the SP is 85
When MP is 1 the SP is (85/100)
When MP is 2,400 the SP is 2,400 x (85/100) = ¤2,040

Question 11: A television has a marked price of ¤18,000 and is sold for ¤15,300. Find the discount percentage.

Marked Price (MP) = ¤18,000
Selling Price (SP) = ¤15,300
Discount = MP − SP
= ¤18,000 − ¤15,300
= ¤2,700
Discount % = (Discount ÷ MP) × 100
= (2,700 ÷ 18,000) × 100
= 15%
Therefore, the discount offered is 15%.

Question 12: A bicycle is sold for ¤8,100 after allowing a discount of 10%. Find its marked price.

Selling Price (SP) = ¤8,100
Discount = 10%
Selling Price = 90% of Marked Price
Marked Price = SP × 100 ÷ 90
= 8,100 × 100 ÷ 90
= ¤9,000
Therefore, the marked price of the bicycle is ¤9,000.

Question 13: A refrigerator has a marked price of ¤32,500 and is sold for ¤29,250. Find the discount amount.

Marked Price (MP) = ¤32,500
Selling Price (SP) = ¤29,250
Discount = MP − SP
= ¤32,500 − ¤29,250
= ¤3,250
Therefore, the discount amount is ¤3,250.

Question 14: A shopkeeper buys a washing machine for ¤18,000. He marks it at ¤24,000 and offers a discount of 10%. Find the profit earned.

Cost Price (CP) = ¤18,000
Marked Price (MP) = ¤24,000
Discount = 10%
Selling Price
= 24,000 × (100 − 10) ÷ 100
= ¤21,600
Profit = SP − CP
= ¤21,600 − ¤18,000
= ¤3,600
Therefore, the profit earned is ¤3,600.

Question 15: A trader purchases an article for ¤5,000 and marks it at ¤5,500. He offers a discount of 20%. Find the loss incurred.

Marked Price (MP) = ¤5,500
Discount = 20%
Selling Price
= 5,500 × 80 ÷ 100
= ¤4,400
Loss = CP − SP
= ¤5,000 − ¤4,400
= ¤600
Therefore, the trader suffers a loss of ¤600.

Question 16: A customer can buy a sofa at either: 25% discount on the marked price, or ¤4,500 off the marked price. If the marked price is ¤18,000, which offer is better?

First offer:
Discount = 25% of ¤18,000
= ¤4,500
Second offer:
Discount = ¤4,500
Both offers give the same discount.
Therefore, both offers are equally beneficial.

Question 17: A store offers the following discounts on a laptop with a marked price of ¤40,000:
Offer A: 15% discount
Offer B: Flat discount of ¤5,500
Which offer gives a lower selling price?

Offer A
Discount = 15% of ¤40,000
= ¤6,000
Selling Price = ¤40,000 − ¤6,000
= ¤34,000
Offer B
Selling Price = ¤40,000 − ¤5,500
= ¤34,500
Offer A gives the lower selling price.
Therefore, Offer A is more beneficial to the customer.

Question 18: A jacket has a marked price of ¤5,000. A shopkeeper offers two successive discounts of 10% and 20%. Find the selling price.

Marked Price (MP) = ¤5,000
After the first discount of 10%:
Selling Price = 5,000 × (100 − 10) ÷ 100
= 5,000 × 90 ÷ 100
= ¤4,500
After the second discount of 20%:
Selling Price = 4,500 × (100 − 20) ÷ 100
= 4,500 × 80 ÷ 100
= ¤3,600
Therefore, the selling price is ¤3,600.

Alternate:
Let MP = 1
After 1st discount of 10% SP = 1 x 0.90
After 2nd discount of 20% SP = (1 x 0.90) x 0.80
So the SP on MP of ¤5,000 = 5,000 x 0.90 x 0.80 = ¤3,600

Question 19: A store offers successive discounts of 15% and 20% on a television. Find the equivalent single discount.

Equivalent Discount %
= 15 + 20 − (15 × 20) ÷ 100
= 35 − 3
= 32%
Therefore, the equivalent single discount is 32%.

Alternate:
Let MP = 100
Intermediate price after 1st discount = [100 x (100 – 15)]/100 = 85
Final SP after 2nd discount = [85 x (100 – 20)]/100 = 68
So equivalent discount = 100 – 68 = 32%

Question 20: After successive discounts of 20% and 10%, a refrigerator is sold for ¤21,600. Find its marked price.

Equivalent Discount
= 20 + 10 − (20 × 10) ÷ 100
= 30 − 2
= 28%
Therefore, the selling price is 72% of the marked price.
Marked Price
= 21,600 × 100 ÷ 72
= ¤30,000
Therefore, the marked price is ¤30,000.

Question 21: A shopkeeper first gives a discount of 20% and then another discount of x%. If the overall discount is 28%, find the value of x.

Equivalent Discount
= First Discount + Second Discount − (First Discount × Second Discount) ÷ 100
28 = 20 + x − (20x ÷ 100)
28 = 20 + x − 0.2x
8 = 0.8x
x = 10
Therefore, the second discount is 10%.

Question 22: A computer has a marked price of ¤80,000. Successive discounts of 10%, 5% and 10% are offered. Find the final selling price.

After the first discount:
80,000 × 90 ÷ 100
= ¤72,000
After the second discount:
72,000 × 95 ÷ 100
= ¤68,400
After the third discount:
68,400 × 90 ÷ 100
= ¤61,560
Therefore, the final selling price is ¤61,560.

Question 23: A shop offers two discount schemes on a sofa with a marked price of ¤25,000.
Scheme A: Single discount of 30%
Scheme B: Two successive discounts of 20% and 10%
Which scheme offers the lower selling price?

Scheme A
Selling Price
= 25,000 × (100 − 30) ÷ 100
= 25,000 × 70 ÷ 100
= ¤17,500
Scheme B
Equivalent Discount
= 20 + 10 − (20 × 10) ÷ 100
= 30 − 2
= 28%
Selling Price
= 25,000 × 72 ÷ 100
= ¤18,000
Since ¤17,500 < ¤18,000,
Scheme A offers the lower selling price and is more beneficial to the customer.

Question 24: A shopkeeper buys an article for ¤2,500. He marks it at ¤3,200 and offers a discount of 10%. Find the profit earned.

Cost Price (CP) = ¤2,500
Marked Price (MP) = ¤3,200
Selling Price (SP)
= 3,200 × (100 − 10) ÷ 100
= 3,200 × 90 ÷ 100
= ¤2,880
Profit = SP − CP
= ¤2,880 − ¤2,500
= ¤380
Therefore, the profit earned is ¤380.

Question 25: An article is purchased for ¤4,000. It is marked at ¤5,000 and sold after allowing a discount of 10%. Find the profit percentage.

Selling Price = 5,000 × 90 ÷ 100
= ¤4,500
Profit = ¤4,500 − ¤4,000
= ¤500
Profit %
= (500 ÷ 4,000) × 100
= 12.5%
Therefore, the profit percentage is 12.5%.

Question 26: A trader marks an article at ¤6,000. After allowing a discount of 20%, he still earns a profit of 20%. Find the cost price.

Selling Price
= 6,000 × 80 ÷ 100
= ¤4,800
Selling Price = 120% of Cost Price
CP = 4,800 × 100 ÷ 120
= ¤4,000
Therefore, the cost price is ¤4,000.

Question 27: A shopkeeper buys an article for ¤5,000. He wants to earn a profit of 25% even after giving a discount of 20%. Find the marked price.

Required Selling Price
= 5,000 × 125 ÷ 100
= ¤6,250
Selling Price = 80% of Marked Price
MP = 6,250 × 100 ÷ 80
= ¤7,812.50
Therefore, the marked price should be ¤7,812.50.

Question 28: A trader purchases an article for ¤8,000 and marks it at ¤10,000. If he earns a profit of 12.5%, find the discount percentage.

Selling Price
= 8,000 × 112.5 ÷ 100
= ¤9,000
Discount
= 10,000 − 9,000
= ¤1,000
Discount %
= (1,000 ÷ 10,000) × 100
= 10%
Therefore, the discount percentage is 10%.

Question 29: An article is purchased for ¤12,000 and marked at ¤15,000. What is the maximum discount that can be offered without incurring a loss?

To avoid a loss,
Selling Price = Cost Price
= ¤12,000
Discount
= 15,000 − 12,000
= ¤3,000
Discount %
= (3,000 ÷ 15,000) × 100
= 20%
Therefore, the maximum discount that can be offered is 20%.

Question 30: A shopkeeper buys an article for ¤2,000. He increases the cost price by 40% to fix the marked price and then offers a discount of 10%. Find his profit percentage.

Marked Price
= 2,000 × 140 ÷ 100
= ¤2,800
Selling Price
= 2,800 × 90 ÷ 100
= ¤2,520
Profit
= 2,520 − 2,000
= ¤520
Profit %
= (520 ÷ 2,000) × 100
= 26%
Therefore, the profit percentage is 26%.

Question 31: A trader purchases an article for ¤8,000. He first increases its value by 20% and then suffers a loss of 10% on the increased value. Find the final selling price.

Cost Price (CP) = ¤8,000
After a profit of 20%:
New Price
= 8,000 × 120 ÷ 100
= ¤9,600
After a loss of 10%:
Selling Price
= 9,600 × 90 ÷ 100
= ¤8,640
Therefore, the final selling price is ¤8,640.

Question 32: A dishonest shopkeeper buys rice at ¤80 per kg but uses a weight of 900 g instead of 1 kg while selling at ¤80 per kg. Find his profit percentage.

The shopkeeper charges for 1 kg but actually gives only 900 g.
Cost of 900 g
= 80 × 900 ÷ 1000
= ¤72
Selling Price = ¤80
Profit = 80 − 72
= ¤8
Profit % = (8 ÷ 72) × 100
= 11.11%
Therefore, the profit percentage is 11.11%.

Question 33: A dishonest trader uses a weight of 1.1 kg instead of 1 kg while buying grain. If the cost price is ¤100 per kg, find his gain percentage.

He pays for 1 kg but actually receives 1.1 kg.
Cost of 1.1 kg = ¤100
Actual cost of 1 kg
= 100 ÷ 1.1
= ¤90.91
Gain = 100 − 90.91
= ¤9.09
Gain % = (9.09 ÷ 90.91) × 100
= 10%
Therefore, the gain percentage is 10%.

Question 34: A trader uses a weight of 1.05 kg while buying and 950 g while selling. Find his overall gain percentage.

Assume the market price is ¤100 per kg.
While buying,
He receives 1.05 kg for ¤100.
Actual cost of 1 kg
= 100 ÷ 1.05
= ¤95.24
While selling,
He gives only 950 g.
Cost of 950 g
= 95.24 × 950 ÷ 1000
= ¤90.48
Selling Price = ¤100
Profit = 100 − 90.48
= ¤9.52
Profit % = (9.52 ÷ 90.48) × 100
≈ 10.53%
Therefore, the overall gain percentage is approximately 10.53%.

Question 35: A shopkeeper sells sugar at its cost price but gives only 800 g instead of 1 kg. Find his profit percentage.

Assume the cost price of 1 kg is ¤100.
Cost of 800 g = ¤80
Selling Price = ¤100
Profit = ¤20
Profit % = (20 ÷ 80) × 100
= 25%
Therefore, the profit percentage is 25%.

Question 36: A milk vendor charges the price of 1 litre but supplies only 900 mL. Find his profit percentage.

Assume the cost price of 1 litre is ¤60.
Cost of 900 mL
= 60 × 900 ÷ 1000
= ¤54
Selling Price = ¤60
Profit = ¤6
Profit %
= (6 ÷ 54) × 100
= 11.11%
Therefore, the profit percentage is 11.11%.

Question 37: A trader earns a profit of 20% on the marked selling price and also gives only 900 g instead of 1 kg. Find his overall profit percentage.

Assume the cost price of 1 kg = ¤100.
Selling Price after 20% profit = ¤120
Cost of 900 g
= 100 × 900 ÷ 1000
= ¤90
Profit = 120 − 90
= ¤30
Profit % = (30 ÷ 90) × 100
= 33.33%
Therefore, the overall profit percentage is 33.33%.

Question 38: A dishonest dealer sells an article at cost price but earns a profit of 25% by using false weights. How many grams does he actually give instead of 1 kg?

Assume the cost price of 1 kg = ¤100.
Profit = 25%
Therefore,
Cost of actual quantity supplied
= 100 ÷ 1.25
= ¤80
Since ¤80 corresponds to the actual quantity,
Actual quantity = 800 g
Therefore, he supplies only 800 g instead of 1 kg.

Question 39: A shopkeeper buys pulses at ¤120 per kg and marks them up by 25%. He then offers a discount of 10% but supplies only 900 g instead of 1 kg. Find his overall profit percentage.

Cost Price (CP) of 1 kg = ¤120
Marked Price
= 120 × 125 ÷ 100
= ¤150
Selling Price after discount
= 150 × 90 ÷ 100
= ¤135
Cost of 900 g
= 120 × 900 ÷ 1000
= ¤108
Profit
= 135 − 108
= ¤27
Profit % = (27 ÷ 108) × 100
= 25%
Therefore, the overall profit percentage is 25%.

Question 40: A dishonest dealer sells sugar at cost price but earns a profit of 20% by using a false weight. How many grams does he actually give instead of 1 kg?

Assume the cost price of 1 kg = ¤100.
Since he earns a profit of 20%,
Cost of the quantity actually supplied
= 100 ÷ 1.20
= ¤83.33
Actual quantity
= (83.33 ÷ 100) × 1000
≈ 833.33 g
Therefore, he actually gives approximately 833.33 g instead of 1 kg.

Question 41: A trader buys rice at ¤90 per kg and gives only 900 g instead of 1 kg. If he wants to earn an overall profit of 25%, at what price should he sell 1 kg (as claimed)?

Cost of 900 g
= 90 × 900 ÷ 1000
= ¤81
Required Selling Price
= 81 × 125 ÷ 100
= ¤101.25
Therefore, he should charge ¤101.25 per kg.

Question 42: A dishonest trader uses a weight of 1.1 kg while buying and 900 g while selling. If the market price is the same for buying and selling, find his overall profit percentage.

Assume the market price = ¤100 per kg.
While buying,
He receives 1.1 kg for ¤100.
Actual cost of 1 kg
= 100 ÷ 1.1
= ¤90.91
Cost of 900 g
= 90.91 × 900 ÷ 1000
= ¤81.82
Selling Price = ¤100
Profit = 100 − 81.82
= ¤18.18
Profit % = (18.18 ÷ 81.82) × 100
≈ 22.22%
Therefore, the overall profit percentage is approximately 22.22%.

Question 43: A shopkeeper marks an article at ¤500 per kg and offers a discount of 10%. He supplies only 800 g instead of 1 kg. If the cost price is ¤360 per kg, find his overall profit percentage.

Selling Price
= 500 × 90 ÷ 100
= ¤450
Cost of 800 g
= 360 × 800 ÷ 1000
= ¤288
Profit
= 450 − 288
= ¤162
Profit % = (162 ÷ 288) × 100
= 56.25%
Therefore, the overall profit percentage is 56.25%.

Question 44: A dishonest dealer supplies only 900 g instead of 1 kg and sells at ¤180 per kg. If his overall profit is 20%, find the cost price per kg.

Let the cost price be ¤x per kg.
Cost of 900 g = 0.9x
Selling Price = ¤180
Since profit is 20%,
180 = 0.9x × 120 ÷ 100
180 = 1.08x
x = 180 ÷ 1.08
= ¤166.67
Therefore, the cost price is ¤166.67 per kg.

Question 45: A trader buys wheat at ¤80 per kg. He increases the price by 15% and also supplies only 950 g instead of 1 kg. Find the overall profit percentage.

Selling Price
= 80 × 115 ÷ 100
= ¤92
Cost of 950 g
= 80 × 950 ÷ 1000
= ¤76
Profit = 92 − 76
= ¤16
Profit % = (16 ÷ 76) × 100
≈ 21.05%
Therefore, the overall profit percentage is approximately 21.05%.

Question 46: A trader earns an overall profit of 33⅓% by using false weights while selling at cost price. How many grams does he actually supply instead of 1 kg?

Assume the cost price of 1 kg = ¤100.
Since profit is 33⅓%,
Cost of actual quantity supplied
= 100 ÷ (4/3)
= ¤75
Actual quantity
= (75 ÷ 100) × 1000
= 750 g
Therefore, he actually supplies 750 g instead of 1 kg.

Question 47: A dishonest dealer uses a weight of 1.2 kg while buying and 800 g while selling. If the market rate is unchanged, find his overall profit percentage.

Assume the market rate = ¤120 per kg.
While buying,
He receives 1.2 kg for ¤120.
Actual cost of 1 kg
= 120 ÷ 1.2
= ¤100
Cost of 800 g
= 100 × 800 ÷ 1000
= ¤80
Selling Price = ¤120
Profit = 120 − 80
= ¤40
Profit % = (40 ÷ 80) × 100
= 50%
Therefore, the overall profit percentage is 50%.

Question 48: A shopkeeper buys sugar at ¤80 per kg but sells only 900 g as 1 kg for the same price. Find his profit percentage.

Cost of 900 g
= 80 × 900 ÷ 1000
= ¤72
Selling Price = ¤80
Profit = 80 − 72
= ¤8
Profit %
= (8 ÷ 72) × 100
= 11.11%
Therefore, the profit percentage is 11.11%.

Question 49: A trader reduces the quantity of tea by 5% but charges the price of the original quantity. Find his profit percentage.

Assume the cost price of 1 kg = ¤100.
Quantity supplied = 95% of 1 kg
Cost of quantity supplied = ¤95
Selling Price = ¤100
Profit = ¤100 − ¤95
= ¤5
Profit %
= (5 ÷ 95) × 100
≈ 5.26%
Therefore, the profit percentage is approximately 5.26%.

Question 50: A trader advertises “20% Extra Quantity Free” instead of giving a discount. If the selling price remains unchanged, what is the effective discount percentage?

Assume a customer pays for 100 units.
Extra quantity = 20 units
Total quantity received = 120 units
Effective price per unit
= 100 ÷ 120
= 83.33%
Effective discount
= 100 − 83.33
= 16.67%
Therefore, offering 20% extra quantity is equivalent to a discount of 16.67%.

Question 51: A trader increases the selling price of oil by 10% and also supplies only 900 mL instead of 1 litre. Find the overall profit percentage.

Assume the cost price of 1 litre = ¤100.
Selling Price = 100 × 110 ÷ 100
= ¤110
Cost of 900 mL
= 100 × 900 ÷ 1000
= ¤90
Profit = 110 − 90
= ¤20
Profit % = (20 ÷ 90) × 100
= 22.22%
Therefore, the overall profit percentage is 22.22%.

Question 52: A shopkeeper sells two articles for ¤2,400 each. He earns a profit of 20% on one article and incurs a loss of 20% on the other. Find his overall profit or loss.

For the first article,
CP = 2,400 × 100 ÷ 120
= ¤2,000
For the second article,
CP = 2,400 × 100 ÷ 80
= ¤3,000
Total Cost Price
= 2,000 + 3,000
= ¤5,000
Total Selling Price
= 2,400 + 2,400
= ¤4,800
Loss = 5,000 − 4,800
= ¤200
Loss % = (200 ÷ 5,000) × 100
= 4%
Therefore, the shopkeeper incurs a loss of 4%.

Question 53: A trader buys two articles for ¤4,000 and ¤6,000 respectively. He sells the first article at a profit of 20%. If his overall profit is 15%, find the selling price of the second article.

Total Cost Price
= 4,000 + 6,000
= ¤10,000
Overall Selling Price
= 10,000 × 115 ÷ 100
= ¤11,500
Selling Price of first article
= 4,000 × 120 ÷ 100
= ¤4,800
Selling Price of second article
= 11,500 − 4,800
= ¤6,700
Therefore, the selling price of the second article is ¤6,700.

Question 54: A trader sells two articles for ¤3,000 each. He earns a profit of 25% on the first article and incurs an overall profit of ¤300. Find the cost price of the second article.

Selling Price of first article
= ¤3,000
Cost Price of first article
= 3,000 × 100 ÷ 125
= ¤2,400
Total Selling Price
= 3,000 + 3,000
= ¤6,000
Total Cost Price
= 6,000 − 300
= ¤5,700
Cost Price of second article
= 5,700 − 2,400
= ¤3,300
Therefore, the cost price of the second article is ¤3,300.

Question 55: A retailer purchases 100 notebooks at ¤40 each. He sells 60 notebooks at a profit of 25% and the remaining 40 notebooks at a loss of 10%. Find the overall profit percentage.

Total Cost Price = 100 × 40
= ¤4,000
Selling Price of 60 notebooks
= 60 × (40 × 125 ÷ 100)
= 60 × 50
= ¤3,000
Selling Price of 40 notebooks
= 40 × (40 × 90 ÷ 100)
= 40 × 36
= ¤1,440
Total Selling Price
= 3,000 + 1,440
= ¤4,440
Profit = 4,440 − 4,000
= ¤440
Profit % = (440 ÷ 4,000) × 100
= 11%
Therefore, the retailer earns an overall profit of 11%.

Question 56: A trader buys two articles for ¤4,000 and ¤6,000 respectively. He earns a profit of 20% on the first article. At what price should he sell the second article so that there is neither overall profit nor loss?

Selling Price of the first article
= 4,000 × 120 ÷ 100
= ¤4,800
Total Cost Price
= 4,000 + 6,000
= ¤10,000
For no profit or loss,
Total Selling Price = ¤10,000
Selling Price of the second article
= 10,000 − 4,800
= ¤5,200
Therefore, the second article should be sold for ¤5,200.

Question 57: A manufacturer produces a chair at a manufacturing cost of ¤1,200. He wants to earn a profit of 25% on the manufacturing cost. Find the selling price.

Manufacturing Cost (MC) = ¤1,200
Profit = 25%
Selling Price (SP)
= 1,200 × 125 ÷ 100
= ¤1,500
Therefore, the selling price of the chair is ¤1,500.

Question 58: The manufacturing cost of a machine is ¤20,000. Due to an increase in the price of raw materials, the manufacturing cost increases by 15%. If the manufacturer continues to earn a profit of 20% on the new manufacturing cost, find the new selling price.

New Manufacturing Cost
= 20,000 × 115 ÷ 100
= ¤23,000
Selling Price
= 23,000 × 120 ÷ 100
= ¤27,600
Therefore, the new selling price is ¤27,600.

Question 59: A wholesaler purchases grain from a supplier. While buying, the wholesaler uses a fraudulent scale that records 1 kg when it actually weighs 1.2 kg. The wholesaler then increases the price per kilogram by 25%. While selling, the wholesaler uses another faulty scale that delivers only 900 g instead of 1 kg. Finally, the wholesaler offers a discount of 10% on the marked price. Find the wholesaler’s overall profit percentage.

Assume the market price of grain is ¤100 per kg.
Step 1: Buying Phase
The wholesaler pays for 1 kg but actually receives 1.2 kg.
Therefore, Cost of 1.2 kg = ¤100
Step 2: Selling Price
The wholesaler marks up the price by 25%.
Marked Price = ¤100 × 125%
= ¤125
A discount of 10% is then offered.
Selling Price = ¤125 × 90%
= ¤112.50
Thus, the wholesaler receives ¤112.50 for every nominal 1 kg sold.
Step 3: Selling Phase
Instead of supplying 1 kg, the wholesaler actually delivers only 900 g (0.9 kg).
Therefore, the 1.2 kg purchased can be sold as:
Number of nominal kilograms sold
= 1.2 ÷ 0.9
= 4/3
Step 4: Total Revenue
Revenue = (4/3) × ¤112.50
= ¤150
Step 5: Overall Profit
Total Cost Price = ¤100
Total Selling Price = ¤150
Profit = 150 − 100
= ¤50
Profit Percentage
= (50 ÷ 100) × 100
= 50%
Therefore, the wholesaler’s overall profit percentage is 50%.

Question 60: A merchant buys a bulk inventory of perishable fruit for ¤12,000. Due to inadequate storage conditions, 20% of the fruit spoils completely and has to be discarded. The merchant fixes the selling price of the remaining fruit such that selling half of the usable stock recovers the entire initial investment of ¤12,000.
Later, the merchant sells the remaining half of the usable stock at a discount due to the fruit becoming overripe. If the merchant makes an overall profit of 20% on the entire transaction, find the discount percentage offered on the overripe batch compared to its marked selling price.

Step 1: Calculate the Required Total Revenue
Initial Cost Price (CP) = ¤12,000
Overall Profit = 20%
Required Total Selling Price
= 12,000 × 120 ÷ 100
= ¤14,400
Step 2: Calculate Usable Quantity
Assume total quantity of fruit = 100 units.
Spoiled fruit = 20%
= 20 units
Usable fruit = 100 − 20
= 80 units
Step 3: Find the Marked Selling Price
Half of usable fruit
= 80 ÷ 2
= 40 units
The merchant recovers his entire investment by selling these 40 units.
Revenue from 40 units = ¤12,000
Therefore, marked selling price per unit
= 12,000 ÷ 40
= ¤300 per unit
Step 4: Find Revenue from Discounted Batch
Remaining usable fruit = 40 units
Total revenue required = ¤14,400
Revenue already earned = ¤12,000
Required revenue from remaining batch
= 14,400 − 12,000
= ¤2,400
Discounted selling price per unit
= 2,400 ÷ 40
= ¤60 per unit
Step 5: Calculate Discount Percentage
Marked Price per unit = ¤300
Discounted Price per unit = ¤60
Discount = 300 − 60
= ¤240
Discount Percentage
= (240 ÷ 300) × 100
= 80%
Therefore, the merchant offered an 80% discount on the overripe batch.

Question 61: A manufacturer sells a machine to a distributor at a profit of 20%. The distributor sells it to a wholesaler at a loss of 10%. The wholesaler sells it to a retailer at a profit of 25%. The retailer then marks up the price by 30% and fixes the marked price. However, to attract customers, the retailer offers a promotional discount on the machine.
If the final price paid by the consumer is exactly equal to the price originally paid by the distributor to the manufacturer, find the discount percentage offered by the retailer.

Let the manufacturing cost of the machine be ¤M.
Step 1: Track the Price Through the Supply Chain
Manufacturer’s Cost Price = ¤M
The manufacturer earns a profit of 20%.
Price paid by distributor
= M × 120 ÷ 100
= ¤1.2M
The distributor sells at a loss of 10%.
Price paid by wholesaler
= 1.2M × 90 ÷ 100
= ¤1.08M
The wholesaler earns a profit of 25%.
Price paid by retailer
= 1.08M × 125 ÷ 100
= ¤1.35M
Step 2: Calculate the Retailer’s Marked Price
The retailer increases the price by 30%.
Marked Price
= 1.35M × 130 ÷ 100
= ¤1.755M
Let the discount factor be D.
Final Selling Price
= 1.755M × D
Step 3: Apply the Given Condition
The consumer pays the same price that the distributor originally paid.
Therefore,
1.755M × D = 1.2M
Cancelling M,
D = 1.2 ÷ 1.755
D = 1200 ÷ 1755
D = 80 ÷ 117
Step 4: Calculate Discount Percentage
Discount %
= (1 − 80 ÷ 117) × 100
= (37 ÷ 117) × 100
≈ 31.62%
Therefore, the promotional discount offered by the retailer was approximately 31.62%.

Question 62: A milkman buys pure milk at ¤100 per litre. He adds water free of cost, increasing the total volume of the mixture by 25%. He then increases the selling price of the mixture by 12% compared to the original price of pure milk. After offering a discount of 5% on the marked price, he sells the mixture using a faulty measuring container that shows 1 litre but actually delivers only 950 mL.
Find the milkman’s overall profit percentage.

Assume the milkman buys 1 litre of pure milk.
Step 1: Calculate the Cost Price
Cost of 1 litre milk = ¤100
Step 2: Calculate the Mixture Volume
He adds water to increase volume by 25%.
Total mixture volume
= 1 × 125 ÷ 100
= 1.25 litres
The total cost remains: = ¤100
Step 3: Calculate the Effective Selling Price
Original price per litre = ¤100
After 12% increase:
Marked Price
= 100 × 112 ÷ 100
= ¤112
After 5% discount:
Actual selling price per billed litre
= 112 × 95 ÷ 100
= ¤106.40
Step 4: Account for Faulty Measurement
The container shows 1 litre but delivers only 950 mL.
Therefore, actual quantity delivered per billed litre
= 0.95 litre
From 1.25 litres of mixture, the milkman can bill:
= 1.25 ÷ 0.95
= 25/19 litres
Step 5: Calculate Total Revenue
Revenue
= (25/19) × 106.40
= ¤140
Step 6: Calculate Profit Percentage
Cost Price
= ¤100
Selling Price
= ¤140
Profit
= 140 − 100
= ¤40
Profit %
= (40 ÷ 100) × 100
= 40%
Therefore, the milkman’s overall profit percentage is 40%.

Question 63: A merchant purchases grain from a supplier. While purchasing, he uses a faulty weighing scale that records 1 kg when the actual quantity received is 1.15 kg. While selling to customers, he uses another faulty scale that displays a weight 10% higher than the actual quantity delivered.
To attract customers, the merchant increases the price by 40% over his original cost price per kilogram and offers the following discount scheme:
○ Buy up to 2 kg: 10% discount
○ Buy more than 2 kg: 20% discount on the total bill
A customer purchases grain weighing 5 kg according to the merchant’s scale.
Find the merchant’s actual profit percentage on this transaction.

Assume the cost price of 1 kg of grain = ¤100.
Step 1: Buying Phase
The merchant pays ¤100 but receives 1.15 kg.
Therefore,
Cost of 1.15 kg
= ¤100
The customer buys 5 kg according to the merchant’s scale.
Step 2: Actual Quantity Delivered
The merchant’s scale shows 10% more than the actual quantity.
Therefore,
Displayed weight = Actual weight × 110%
5 = Actual weight × 1.10
Actual weight delivered
= 5 ÷ 1.10
= 50/11 kg
≈ 4.545 kg
Step 3: Calculate Selling Price
Original cost price per kg
= ¤100
After 40% mark-up:
Marked Price
= 100 × 140 ÷ 100
= ¤140 per nominal kg
Since the customer buys more than 2 kg,
Discount = 20%
Actual selling price
= 140 × 80 ÷ 100
= ¤112 per nominal kg
Total revenue
= 5 × 112
= ¤560
Step 4: Calculate Cost of Actual Quantity Delivered
The merchant’s effective cost per kg:
Cost of 1.15 kg = ¤100
Cost of 1 kg
= 100 ÷ 1.15
= ¤86.9565
Cost of 50/11 kg
= (100 ÷ 1.15) × (50/11)
≈ ¤395.26
Step 5: Calculate Profit Percentage
Profit = 560 − 395.26
= ¤164.74
Profit % = (164.74 ÷ 395.26) × 100
≈ 41.68%
Therefore, the merchant’s actual profit percentage on this transaction is approximately 41.68%.

Question 64: An oil distributor purchases a container of pure oil with an initial volume of 100 litres at a cost of ¤100 per litre. During transportation, 10% of the oil leaks out. To restore the original volume, the distributor adds 10 litres of a substitute liquid that costs only 20% of the price of pure oil per litre.
The distributor then marks up the selling price of the mixture by 25% compared to the original price of pure oil. Before the mixture reaches customers, 5% of the total volume is lost due to evaporation.
Find the distributor’s overall profit percentage on the initial investment.

Step 1: Calculate Initial Investment
Initial volume of pure oil = 100 litres
Cost per litre = ¤100
Initial Investment
= 100 × 100
= ¤10,000
Step 2: Account for Leakage During Transport
Oil leaked = 10% of 100 litres
= 10 litres
Remaining pure oil
= 100 − 10
= 90 litres
Step 3: Add Substitute Liquid
To restore the volume, the distributor adds:
Substitute liquid = 10 litres
Cost of substitute per litre
= 20% of ¤100
= ¤20
Cost of substitute
= 10 × 20
= ¤200
Step 4: Calculate Total Cost of Mixture
Cost of pure oil
= ¤10,000
Cost of substitute = ¤200
Total Cost = ¤10,200
Total mixture volume
= 100 litres
Step 5: Calculate Selling Price
Original price per litre
= ¤100
After 25% mark-up:
Marked Selling Price
= 100 × 125 ÷ 100
= ¤125 per litre
Step 6: Account for Evaporation Loss
Volume lost
= 5% of 100 litres
= 5 litres
Final usable volume
= 100 − 5
= 95 litres
Step 7: Calculate Revenue
Total Revenue
= 95 × 125
= ¤11,875
Step 8: Calculate Profit Percentage
Profit = 11,875 − 10,200
= ¤1,675
Profit % = (1,675 ÷ 10,200) × 100
≈ 16.42%
Therefore, the distributor earns an overall profit of approximately 16.42%.

Question 65: An antique item passes through a chain of four dealers: A, B, C and D.
Dealer A sells the item to Dealer B at a profit of p%. Dealer B sells it to Dealer C at a loss of p%. Dealer C then sells it to Dealer D at a profit of p%. Finally, Dealer D sells the item to a museum at a loss of p%.
If the museum purchases the antique for exactly 92.16% of the amount originally paid by Dealer A, find the value of p.

Let the price originally paid by Dealer A be ¤x.
A profit of p% gives a multiplier:
(1 + p/100)
A loss of p% gives a multiplier:
(1 − p/100)
Step 1: Apply the Four Transactions
Final Price
= ¤x × (1 + p/100) × (1 − p/100) × (1 + p/100) × (1 − p/100)
Grouping the terms:
= ¤x × [(1 + p/100)(1 − p/100)]²
Using the identity:
(a + b)(a − b) = a² − b²
we get:
Final Price
= ¤x × (1 − p²/10000)²
Step 2: Apply the Given Condition
The museum pays 92.16% of the original price.
Therefore,
¤x × (1 − p²/10000)² = 0.9216 × ¤x
Cancelling ¤x:
(1 − p²/10000)² = 0.9216
Taking square root:
1 − p²/10000 = √0.9216
1 − p²/10000 = 0.96
Step 3: Solve for p
p²/10000 = 1 − 0.96
p²/10000 = 0.04
p² = 400
p = √400
p = 20
Therefore, the value of p is 20%.

Question 66: A collector sells a rare artifact to a shopkeeper at a profit of 25%. A year later, the collector decides to buy back the same artifact. The shopkeeper marks up the purchase price by 40% but allows the collector to use a promotional coupon that gives a 10% discount on the marked price.
If the collector pays ¤315 more than the original cost of the artifact before selling it, find the total profit earned by the shopkeeper.

Let the collector’s original cost price of the artifact be ¤C.
Step 1: Collector Sells to the Shopkeeper
The collector earns a profit of 25%.
Therefore,
Shopkeeper’s Cost Price = 1.25C
Step 2: Shopkeeper Sells Back to the Collector
The shopkeeper marks up the price by 40%.
Marked Price = 1.25C × 1.40
= 1.75C
The collector receives a 10% discount.
Final Selling Price
= 1.75C × 0.90
= 1.575C
Step 3: Apply the Given Condition
The collector pays ¤315 more than the original cost price.
Therefore,
1.575C − C = 315
0.575C = 315
C = 315 ÷ 0.575
C ≈ ¤547.83
Step 4: Calculate the Shopkeeper’s Profit
Shopkeeper’s Cost Price = 1.25C
Shopkeeper’s Selling Price = 1.575C
Profit = 1.575C − 1.25C
= 0.325C
= 0.325 × 547.83
≈ ¤178.04
Therefore, the total profit earned by the shopkeeper is approximately ¤178.04.

Question 67: A tech retailer stocks 200 premium smart displays. He plans to earn an overall profit of 10% on the entire inventory. He sells the first 80 units at a profit of 60% and the next 70 units at a profit of 10%. A warehouse flood damages half of the remaining inventory beyond repair. At what profit or loss percentage should he sell each of the remaining undamaged units to achieve his original overall profit target?

Assume the cost price of each smart display is ¤100.
Step 1: Calculate the Total Cost Price
Total number of displays = 200
Cost price per display = ¤100
Total Cost Price = 200 × 100 = ¤20,000
The retailer wants an overall profit of 10%.
Required Total Selling Price
= 20,000 × 110%
= ¤22,000
Step 2: Revenue from the First 80 Displays
Profit = 60%
Selling price per display
= 100 × 160%
= ¤160
Revenue = 80 × 160
= ¤12,800
Step 3: Revenue from the Next 70 Displays
Profit = 10%
Selling price per display
= 100 × 110%
= ¤110
Revenue = 70 × 110
= ¤7,700
Step 4: Calculate the Remaining Inventory
Displays already sold
= 80 + 70
= 150
Displays remaining
= 200 − 150
= 50
Half are damaged beyond repair.
Damaged displays
= 50 ÷ 2
= 25
Undamaged displays remaining
= 50 − 25
= 25
Step 5: Calculate the Revenue Still Required
Revenue already earned
= 12,800 + 7,700
= ¤20,500
Required Total Revenue
= ¤22,000
Revenue still needed
= 22,000 − 20,500
= ¤1,500
Step 6: Find the Selling Price of Each Remaining Display
Remaining undamaged displays
= 25
Selling price per display
= 1,500 ÷ 25
= ¤60
Step 7: Calculate the Profit or Loss Percentage
Cost price per display
= ¤100
Selling price per display
= ¤60
Loss per display
= 100 − 60
= ¤40
Loss Percentage
= (40 ÷ 100) × 100
= 40%
Therefore, each of the remaining undamaged smart displays must be sold at a loss of 40% to achieve the retailer’s original overall profit target of 10%.

Question 68: A manufacturer produces a precision tool. The production cost is divided equally among three components:
⚬ Raw Material
⚬ Energy Consumption
⚬ Manual Labour
During the next financial year, raw material costs increase by 45%, energy costs increase by 30%, while manual labour costs decrease by 15% due to improved efficiency.
Originally, the manufacturer sold the tool at a profit of 25% on the total cost price.
By what percentage must the retail selling price be increased to maintain the same profit margin?

Assume the original total cost price of one precision tool is ¤300.
Since the production cost is divided equally among the three components:
Raw Material = ¤100
Energy Consumption = ¤100
Manual Labour = ¤100
Step 1: Calculate the Revised Production Cost
Raw Material after a 45% increase
= 100 × 145%
= ¤145
Energy Consumption after a 30% increase
= 100 × 130%
= ¤130
Manual Labour after a 15% decrease
= 100 × 85%
= ¤85
Therefore,
New Total Cost Price
= 145 + 130 + 85
= ¤360
Step 2: Calculate the Original Selling Price
Original profit
= 25% of Cost Price
Original Selling Price
= 300 × 125%
= ¤375
Step 3: Calculate the New Selling Price
To maintain the same profit margin of 25%,
New Selling Price
= 360 × 125%
= ¤450
Step 4: Calculate the Required Increase in Selling Price
Increase in Selling Price
= 450 − 375
= ¤75
Percentage Increase
= (75 ÷ 375) × 100
= 20%

Question 69: A manufacturer produces a specialised medical device at a production cost of ¤4,000 per unit. The manufacturer initially sells the device at a profit of 25% on the cost price.
Before the next production cycle, the production cost increases by 18%. At the same time, the government imposes a 12% sales tax, which is calculated on the selling price (before tax).
The manufacturer wants customers to pay exactly the same final price (including tax) as before the tax was introduced.
By how many percentage points does the manufacturer’s profit margin change?

Step 1: Original Selling Price
Cost Price = ¤4,000
Profit = 25%
Selling Price = 4,000 × 125%
= ¤5,000
Since there was no sales tax initially,
Customer’s Final Price
= ¤5,000
Step 2: New Cost Price
Increase in production cost = 18%
New Cost Price = 4,000 × 118%
= ¤4,720
Step 3: Determine the New Selling Price
The customer must still pay ¤5,000, including tax.
Let the required selling price before tax be S.
Since tax is 12%,
S × 112% = 5,000
S = 5,000 ÷ 1.12
≈ ¤4,464.29
Step 4: Determine the New Profit
Profit = 4,464.29 − 4,720
≈ −¤255.71
This is actually a loss.
Loss Percentage
= (255.71 ÷ 4,720) × 100
≈ 5.42%
Originally the manufacturer earned a profit of 25%.
Now the manufacturer incurs a 5.42% loss.
Therefore, the reduction in profit percentage is
25% + 5.42%
= 30.42%

Question 70: A company purchases an industrial machine for ¤9,60,000. The company plans to recover the entire investment by selling products manufactured using the machine over the next three years.
During the first year, the company recovers 35% of the machine’s cost.
During the second year, it recovers 45% of the remaining unrecovered amount.
At the beginning of the third year, the government introduces a subsidy that reimburses 20% of the still unrecovered amount.
What percentage of the original machine cost must the company recover through sales during the third year to completely recover its investment?

Step 1: Original Machine Cost
Machine Cost = ¤9,60,000
Step 2: Recovery During Year 1
Recovered = 35%
= 9,60,000 × 35%
= ¤3,36,000
Balance = 9,60,000 − 3,36,000
= ¤6,24,000
Step 3: Recovery During Year 2
Recovered = 45% of 6,24,000
= 6,24,000 × 45%
= ¤2,80,800
Balance = 6,24,000 − 2,80,800
= ¤3,43,200
Step 4: Government Subsidy
Subsidy = 20% of 3,43,200
= ¤68,640
Remaining amount
= 3,43,200 − 68,640
= ¤2,74,560
Step 5: Percentage of Original Cost
Required Recovery
= ¤2,74,560
Original Machine Cost
= ¤9,60,000
Required Percentage
= (2,74,560 ÷ 9,60,000) × 100
= 28.6%
Therefore, the company must recover 28.6% of the original machine cost through sales during the third year to fully recover its investment.

Question 71: By selling 8 articles, a tradesman makes a loss equal to the cost price of 4 articles. Find his loss percentage.

Let the cost price of each article be ¤100.
Cost price of 8 articles
= 8 × 100
= ¤800
Loss = Cost price of 4 articles
= 4 × 100
= ¤400
Selling Price
= 800 − 400
= ¤400
Loss %
= (Loss ÷ CP) × 100
= (400 ÷ 800) × 100
= 50%
Therefore, the tradesman suffers a loss of 50%.

Question 72: By selling an article at ⁷⁄₁₀ of its actual selling price, a trader makes a profit of 20%. If he sells the article at 20% less than the actual selling price, find his profit or loss percentage.

Let the actual selling price be ¤100.
Selling price at ⁷⁄₁₀ of actual selling price
= 100 × ⁷⁄₁₀ = ¤70
This selling price gives a profit of 20%.
Therefore,
CP = 70 ÷ 1.20 = ¤58.33
New selling price after 20% reduction from actual selling price:
= 100 × 80%
= ¤80
Profit = 80 − 58.33
= ¤21.67
Profit % = (21.67 ÷ 58.33) × 100
≈ 37.15%
Therefore, the trader earns a profit of approximately 37.15%.

Question 73: A man bought an article at a 20% discount on its original price. He then sold it at a 40% increase on his purchase price. The new selling price is what percent more than the original price?

Let the original price be ¤100.
After 20% discount:
Purchase price = 100 − 20 = ¤80
He increases the purchase price by 40%.
Selling price = 80 × 140%
= ¤112
Increase over original price
= 112 − 100 = ¤12
Percentage increase
= (12 ÷ 100) × 100 = 12%
Therefore, the new selling price is 12% more than the original price.

Question 74: The marked price of an article is 10% above its cost price. During a sale, the trader allows a certain discount and suffers a loss of 1%. Find the discount percentage allowed.

Let the cost price be ¤100.
Marked Price = 100 × 110%
= ¤110
The trader suffers a loss of 1%.
Selling Price = 100 × 99%
= ¤99
Discount allowed = 110 − 99
= ¤11
Discount % = (11 ÷ 110) × 100
= 10%
Therefore, the trader allowed a discount of 10%.

Question 75: A dairy trader purchases 30 litres of milk at the rate of ¤8 per litre. He spends an additional ¤10 on processing the milk, after which he obtains 5 kg of cream and 30 litres of toned milk. He sells the cream at ¤30 per kg and the toned milk at ¤4 per litre.
Find the profit earned by the trader in the transaction.

Step 1: Calculate Total Cost
Cost of milk
= 30 × ¤8
= ¤240
Processing cost = ¤10
Total Cost Price
= 240 + 10
= ¤250
Step 2: Calculate Total Revenue
Revenue from cream
= 5 × ¤30
= ¤150
Revenue from toned milk
= 30 × ¤4
= ¤120
Total Selling Price
= 150 + 120
= ¤270
Step 3: Calculate Profit
Profit = Selling Price − Cost Price
= 270 − 250
= ¤20
Step 4: Calculate Profit Percentage
Profit % = (Profit ÷ Cost Price) × 100
= (20 ÷ 250) × 100
= 8%
Therefore, the trader earns a profit of ¤20, which is equal to a profit of 8% on the total investment.

What is Profit and Loss?

Profit and Loss is a concept used to calculate the gain or loss made when an item is bought and sold. When the selling price of an item is higher than its cost price, the difference is called profit. When the selling price is lower than the cost price, the difference is called loss. These concepts help in understanding the financial outcome of transactions and are widely used in business and everyday calculations.

Understanding Cost Price and Selling Price

Profit and Loss is based on the comparison between the Cost Price (CP) and the Selling Price (SP) of an item.
Cost Price (CP): The price at which an item is purchased is called its cost price.
Selling Price (SP): The price at which an item is sold is called its selling price.
When the selling price is greater than the cost price, the seller earns a profit.
Profit = Selling Price − Cost Price
When the selling price is less than the cost price, the seller suffers a loss.
Loss = Cost Price − Selling Price
Example:
A trader buys an article for ¤800 and sells it for ¤950.
CP = ¤800
SP = ¤950
Since SP > CP,
Profit = SP − CP
= ¤950 − ¤800
= ¤150
Therefore, the trader earns a profit of ¤150.

Profit Percentage, Loss Percentage and Relationship Between CP and SP

Profit and loss are generally expressed as percentages of the cost price.
Profit Percentage
Profit % = (Profit ÷ CP) × 100
Loss Percentage
Loss % = (Loss ÷ CP) × 100
The relationship between cost price, selling price and profit/loss can be written as:
When there is profit: SP = CP + Profit
When there is loss: SP = CP − Loss
When profit percentage or loss percentage is given, the selling price can be calculated using:
SP = CP × (100 + Profit %) ÷ 100
SP = CP × (100 − Loss %) ÷ 100

Marked Price and Discount

The Marked Price (MP) is the price printed on an article or the price at which a seller initially lists an item for sale.
A seller may offer a discount on the marked price to attract customers. The price after deducting the discount is called the Selling Price (SP).
Discount = Marked Price − Selling Price
Discount % = (Discount ÷ MP) × 100

Finding Selling Price After Discount

When the marked price and discount percentage are given, the selling price can be calculated using:
SP = MP × (100 − Discount %) ÷ 100
Example:
A watch has a marked price of ¤2,500 and a discount of 20% is offered.
SP = 2,500 × (100 − 20) ÷ 100
= 2,500 × 80 ÷ 100
= ¤2,000
Therefore, the selling price of the watch is ¤2,000.

Successive Discounts

A number is divisible by 6 if it is divisible by both 2 and 3. In other words, the number must be even and the sum of its digits must be divisible by 3.
Example: 540 has 0 in the one’s place, so it is divisible by 2. The sum of its digits (5 + 4 + 0 = 9) is divisible by 3. Therefore, 540 is divisible by 6.

Profit and Loss After Discount

In many real-life situations, a seller decides the marked price, provides a discount, and still earns a profit.
The relationship between these values is:
Selling Price = Marked Price − Discount
and,
Profit = Selling Price − Cost Price
To find the final profit or loss, first calculate the actual selling price after discount and then compare it with the cost price.
Example:
A shopkeeper buys an article for ¤800 and marks it at ¤1,200. He gives a discount of 10%.
Selling Price:
= 1,200 × (100 − 10) ÷ 100
= ¤1,080
Profit:
= SP − CP
= ¤1,080 − ¤800
= ¤280
Therefore, the shopkeeper earns a profit of ¤280.

Profit and Loss in Multiple Transactions

When multiple items are bought or sold, the overall profit or loss is calculated by comparing the total cost price with the total selling price.
Overall Profit = Total SP − Total CP
Overall Loss = Total CP − Total SP
Example:
A trader buys two articles for ¤500 and ¤800 respectively. He sells them for ¤600 and ¤750 respectively.
Total CP = ¤500 + ¤800
= ¤1,300
Total SP = ¤600 + ¤750
= ¤1,350
Profit = Total SP − Total CP
= ¤1,350 − ¤1,300
= ¤50
Therefore, the trader earns an overall profit of ¤50.

Summary of Profit and Loss

Concept	Key Formula / Rule
Cost Price (CP)	The price at which an article is purchased or produced.
Selling Price (SP)	The price at which an article is sold to a customer.
Profit	Profit = SP − CP
Loss	Loss = CP − SP
Profit Percentage	Profit % = (Profit ÷ CP) × 100
Loss Percentage	Loss % = (Loss ÷ CP) × 100
Finding SP	SP = CP × (100 + Profit %) ÷ 100 SP = CP × (100 − Loss %) ÷ 100
Finding CP	CP = SP × 100 ÷ (100 + Profit %) CP = SP × 100 ÷ (100 − Loss %)
Marked Price (MP)	The price printed or displayed on an article before applying any discount.
Discount	Discount = Marked Price − Selling Price
Discount Percentage	Discount % = (Discount ÷ Marked Price) × 100
Successive Discounts	Equivalent discount = a + b − (ab ÷ 100), where a and b are the two discount percentages.
Successive Profit/Loss Changes	For successive changes: Final Value = Initial Value × (1 ± a/100) × (1 ± b/100)
Profit and Loss on Equal Selling Prices	If one article is sold at x% profit and another at x% loss for the same SP, there is always an overall loss.
Overall Profit/Loss in Multiple Transactions	Overall Profit/Loss % = (Total SP − Total CP) ÷ Total CP × 100
Dishonest Dealer Problems	Actual profit may result from incorrect weights, short measurements, or false quantities. Compare actual quantity received and delivered.
Changing Quantity Method	When quantity changes but price remains fixed, compare the actual quantity bought and sold to determine the effective profit or loss.
Weighted Profit/Loss	When multiple items have different profit/loss percentages, calculate total CP and total SP separately before finding the overall percentage.

Common Mistakes

Students often confuse cost price and selling price while calculating profit or loss. Remember that profit or loss is always calculated on the cost price, not on the selling price.
Using the wrong formula for profit and loss percentage. Always remember:
1. Profit % = (Profit ÷ CP) × 100
2. Loss % = (Loss ÷ CP) × 100
Assuming that a discount always results in a loss. A discount is calculated on the marked price, and the final result depends on the relationship between the marked price and cost price.
Adding successive discounts directly. For example, discounts of 20% and 10% do not give a total discount of 30%. The second discount is applied after the first discount has already reduced the price.
Confusing profit percentage with increase in selling price. A 20% increase in selling price does not always mean a 20% profit because profit percentage depends on the cost price.
Calculating overall profit or loss by simply averaging different profit and loss percentages. When multiple transactions are involved, always calculate total cost price and total selling price separately.
Ignoring the effect of quantity in dishonest dealer problems. In such questions, profit may come from incorrect weights or measurements, so compare the actual quantity received and delivered.
Making mistakes in equal profit and loss percentage situations. When two articles are sold at the same selling price with equal profit and loss percentages, the overall result is always a loss, not a profit.
Forgetting to include additional expenses while finding profit or loss. Costs such as transportation, processing charges, packaging, or repair expenses must be added to the cost price.
Applying percentage changes incorrectly in successive profit or loss problems. A 20% increase followed by a 20% decrease does not bring the value back to the original amount.

Practice Questions

Question 1: A retailer purchases an item after receiving a 20% discount on its marked price. He then sells it at a price 30% higher than his purchase price. Find the percentage difference between the final selling price and the original marked price.

Question 2: A shopkeeper sells two articles for the same selling price. On one article, he earns a profit of 25%, while on the other, he suffers a loss of 20%. Find his overall profit or loss percentage.

Question 3: A dishonest dealer claims to sell goods at cost price but uses a weight that is 20% less than the standard weight. Find his actual profit percentage.

Question 4: The price of an article is increased by 20% and then decreased by 20%. If the final price is ¤960, find the original price of the article.

Question 5: A manufacturer increases the cost price of a product by 25% due to a rise in raw material costs. To maintain the same profit percentage, he increases the selling price by ¤500. If the original profit percentage was 20%, find the original cost price.

Question 6: A trader buys an article and marks its price 50% above the cost price. He offers two successive discounts of 20% and 10%. Even after these discounts, he earns a profit of 8%. Find the percentage discount he would need to offer (instead of the two discounts) to earn exactly 5% profit if the marked price remains unchanged.

Question 7: A trader purchases an article at a certain cost price. He marks the article 60% above the cost price and offers two successive discounts of 15% and 20%. After selling the article, he finds that his profit is ¤272. Find the cost price of the article.