Profit and Loss
- A shopkeeper buys 40 bicycles and marks them at 25% above the cost price. He allows a discount of 10% on the marked price for cash sales, and 5% for credit sales. If three-fourth of the stock is sold for cash and the rest for credit, and if the total profit be $ 20250, what is the cost price of a bicycle ?
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Given that , Number of bicycles = 40
Let C.P. of one bicycle be y∴ Marked price of each bicycle = 125 y = 1.25y 100
Discount for cash sale = 10%
Discount for credit sale = 5%∴ S.P. for cash sale = 1.25 y × 90 100
S.P. for cash sale = (1.25 y × 0.9) = 1.125 yS.P. for credit sale = 1.25 y × 90 100
S.P. for credit sale = (1.25 y × 0.95) = 1.1875 y
Number of bicycles sold for cash = 30
Number of bicycles sold on credit = 10
∴ Total S.P. = [1.125 y × 30 + 1.1875y × 10] = 45.625 y
∴ Profit = (45.625 – 40) y = 5.625 y
Correct Option: D
Given that , Number of bicycles = 40
Let C.P. of one bicycle be y∴ Marked price of each bicycle = 125 y = 1.25y 100
Discount for cash sale = 10%
Discount for credit sale = 5%∴ S.P. for cash sale = 1.25 y × 90 100
S.P. for cash sale = (1.25 y × 0.9) = 1.125 yS.P. for credit sale = 1.25 y × 90 100
S.P. for credit sale = (1.25 y × 0.95) = 1.1875 y
Number of bicycles sold for cash = 30
Number of bicycles sold on credit = 10
∴ Total S.P. = [1.125 y × 30 + 1.1875y × 10] = 45.625 y
∴ Profit = (45.625 – 40) y = 5.625 y
But actual profit = $ 20250
∴ 5.625 y = 20250⇒ y = 20250 = $ 3600 5.625
Hence, C.P. of a bicycle = $ 3600
- A defective briefcase costing $ 800 is being sold at a loss of 8%. If the price is further reduced by 5%, find its approximate selling price.
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Given that , C.P. = $ 800
Loss = 8%⇒ SP = $ 800 - 8 × 800 100
SP = $ 800 – 64 = $ 736Reduction 5% = 5 × 736 100
Correct Option: C
Given that , C.P. = $ 800
Loss = 8%⇒ SP = $ 800 - 8 × 800 100
SP = $ 800 – 64 = $ 736Reduction 5% = 5 × 736 100 ∴ Reduced SP = $ 736 – 736 × 5 100
Reduced SP = $ 736 – 36.80 = $ 699.20
∴ Selling price = $ 699.20 ≈ $ 700
- A wholesaler sells 20 pens at the marked price (printed on the article) of 16 pens to a retailer. The retailer in turn sells them at the marked price . Determine the gain or loss per cent to the retailer.
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Let the marked price of 1 pen = $ 100
∴ MP of 20 pens = 20 × 100 = $ 2000
MP of 16 pens = 16 × 100 = $ 1600
CP of 20 pens for retailer = $ 1600
SP of 20 pens for retailer = $ 2000
∴ Profit = 2000 - 1600 = $ 400Profit% = Profit × 100 CP of 20 pens for retailer
Correct Option: B
Let the marked price of 1 pen = $ 100
∴ MP of 20 pens = 20 × 100 = $ 2000
MP of 16 pens = 16 × 100 = $ 1600
CP of 20 pens for retailer = $ 1600
SP of 20 pens for retailer = $ 2000
∴ Profit = 2000 - 1600 = $ 400Profit% = Profit × 100 CP of 20 pens for retailer Profit% = 400 × 100 = 25% 1600
- A shopkeeper reduces the price of his goods by 50% at the time of sale. Initially the price was fixed to get a profit of 25% on selling price after allowing 10% cash discount. Find out his approximate percentage of profit or loss.
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Let initial S.P. = $ 100
profit = 25% of 100 = 25
∵ profit = Initial S.P. - C.P.
∴ C.P. = 100 – 25 = $ 75
Now, when
∴ x = 100 × 100 = $ 1000 90 9 ∴ New S.P. = 50% of $ 1000 i.e., 1000 × 50 9 9 9 New S.P. = $ 500 = $ 55 5 9 9
∴ Loss = $ 75 (Old Price) – $ 55 5 (New S.P.) = $ 19 4 9 9
∴ When
Correct Option: A
Let initial S.P. = $ 100
profit = 25% of 100 = 25
∵ profit = Initial S.P. - C.P.
∴ C.P. = 100 – 25 = $ 75
Now, when∴ x = 100 × 100 = $ 1000 90 9 ∴ New S.P. = 50% of $ 1000 i.e., 1000 × 50 9 9 9 New S.P. = $ 500 = $ 55 5 9 9
∴ Loss = $ 75 (Old Price) – $ 55 5 (New S.P.) = $ 19 4 9 9
∴ When∴y = 100 × 175 75 9 Loss percent = 700 = 25 25 % = 26% (approx) 27 27
- Ram Kumar sold his motor cycle to Mohan at a loss of 28%. Mohan spent $ 1680 on its repairs and sold the motor cycle to Sohan for $ . 35910, thereby, making a profit of 12.5%. Find the cost of the motor cycle for Ram Kumar.
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Let CP of motor cycle for Ram Kumar be x
SP for Ram Kumar = x - 28 x = 72 x 100 100 ∴ Cost for Mohan = 72 x 100
Cost of repairing = $ 1680∴ Total CP for Mohan = $ 72 x + 1680 100
Profit earned by Mohan = 12.5%
SP for Mohan = CP + ProfitSP for Mohan = 72 x + 1680 + 12.5 
72 x + 1680 
100 100 100 
Correct Option: D
Let CP of motor cycle for Ram Kumar be x
SP for Ram Kumar = x - 28 x = 72 x 100 100 ∴ Cost for Mohan = 72 x 100
Cost of repairing = $ 1680∴ Total CP for Mohan = $ 72 x + 1680 100
Profit earned by Mohan = 12.5%
SP for Mohan = CP + ProfitSP for Mohan = 72 x + 1680 + 12.5 72 x + 1680 100 100 100 ⇒ 72x + 1680 = 31920 100 ⇒ x = 30240 × 100 = $ 42000 72
So, the cost price of the motor cycle for Ram Kumar = $ 42,000
