Practice Questions
Concept Explanation
Every commercial transaction in aptitude papers revolves around two prices: what the seller pays (cost price) and what the buyer pays (selling price). Mastering CP and SP is the foundation for profit, loss, discount, and marked-price questions.
Key Definitions
- Cost Price (CP) — the price at which an article is purchased or manufactured.
- Selling Price (SP) — the price at which the article is sold to the customer.
- Profit — when SP > CP, Profit = SP − CP.
- Loss — when CP > SP, Loss = CP − SP.
Percentage Rules (Placement Standard)
In Indian placement exams, profit% and loss% are always calculated on cost price, unless the question explicitly states otherwise.
- Profit% = (Profit / CP) × 100
- Loss% = (Loss / CP) × 100
Forward Formulas
If profit is p% on CP: SP = CP × (100 + p) / 100
If loss is l% on CP: SP = CP × (100 − l) / 100
Reverse Formulas
If SP is given with p% profit on CP: CP = SP × 100 / (100 + p)
If SP is given with l% loss on CP: CP = SP × 100 / (100 − l)
Break-even
When CP = SP, there is neither profit nor loss.
Common Trap
Do not apply profit% on SP unless stated. If CP is 80% of SP, profit% on CP is 25%, not 20%.
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Q1 EasyA man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?ExplanationSP = 1400 × (100 − 15)/100 = 1400 × 0.85 = Rs. 1,190.
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Q2 EasyIn a wholesale assessment, a dealer buys 50 units at Rs. 120 each and sells every unit at Rs. 138. What is the total profit on the transaction?ExplanationProfit per unit = 138 − 120 = Rs. 18. Total profit = 50 × 18 = Rs. 900.
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Q3 EasyA merchant purchases a camera for Rs. 8,500 and sells it for Rs. 7,990. What is the loss incurred on the sale?ExplanationLoss = CP − SP = 8500 − 7990 = Rs. 510.
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Q4 EasyIn an aptitude screening test, an article costing Rs. 960 is sold at a profit of 15% on cost price. What is the selling price?ExplanationSP = 960 × 1.15 = Rs. 1,104.
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Q5 MediumA shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?ExplanationCP = 392 × 100/122.5 = Rs. 320. Profit = 392 − 320 = Rs. 72.
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Q6 MediumAlfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:ExplanationTotal CP = 4700 + 800 = Rs. 5500. Gain = 300. Gain% = (300/5500) × 100 = 5 5/11%.
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Q7 MediumOn selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:Explanation17C − 720 = 5C → 12C = 720 → C = Rs. 60.
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Q8 MediumSam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?ExplanationCP = 20 × 375 = Rs. 7,500. Total toys = 240. SP = 240 × 33 = Rs. 7,920. Profit% = (420/7500) × 100 = 5.6%.
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Q9 MediumA shopkeeper sold a watch for Rs. 2,160, thereby earning a profit of 20% on the cost price. What was the cost price of the watch?ExplanationCP = 2160 × 100/(100 + 20) = 2160 × 100/120 = Rs. 1,800.
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Q10 MediumAn article is sold for Rs. 680 at a loss of 15%. What is the cost price of the article?ExplanationCP = 680 × 100/(100 − 15) = 680 × 100/85 = Rs. 800.
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Q11 MediumDuring a campus placement drill, a trainee finds that an article bought for Rs. 625 is sold at a profit of 12%. What is the selling price?ExplanationSP = 625 × 1.12 = Rs. 700.
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Q12 MediumTwo articles are purchased for Rs. 400 and Rs. 600 respectively. If the first is sold at 25% profit and the second at 10% loss, what is the total selling price?ExplanationSP = 400 × 1.25 + 600 × 0.90 = 500 + 540 = Rs. 1,040.
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Q13 HardIf the selling price of an article is doubled, the profit becomes three times the original profit. What was the original profit percentage on cost price?ExplanationLet CP = C and original SP = S. Then 2S − C = 3(S − C) → S = 2C. Original profit% on CP = 100%.
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Q14 HardAn article is sold for Rs. 495 at a profit of 10%. If the cost price had been Rs. 50 less with the selling price unchanged, what would have been the profit percentage on the new cost price?ExplanationOriginal CP = 495/1.1 = Rs. 450. New CP = Rs. 400. Profit = Rs. 95. Profit% = (95/400) × 100 = 23.75%.
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DS1 Easy
What is the cost price?
Statement IThe article is sold for Rs. 550 at a profit of 10%.
Statement IIThe profit amount is Rs. 50.
ExplanationStatement I: CP = 550 × 100/110 = Rs. 500. Statement II alone does not fix CP without the selling price. -
DS2 Medium
In a retail assessment worksheet, candidates must determine the selling price of an article. What is the selling price?
Statement IThe cost price is Rs. 800 and the profit is 15% on cost price.
Statement IIThe profit amount is Rs. 120.
ExplanationStatement I: SP = 800 × 1.15 = Rs. 920. Statement II alone does not give SP without CP.
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DS3 Medium
A placement trainer asks for the profit percentage reckoned on cost price. What is the profit percentage on cost price?
Statement IThe cost price is Rs. 400 and the selling price is Rs. 460.
Statement IIThe profit amount is Rs. 60.
ExplanationStatement I: (60/400) × 100 = 15%. Statement II alone cannot give profit% without CP. -
DS4 Hard
During a mock interview quantitative round, can the cost price be determined uniquely? What is the cost price?
Statement IThe selling price is 25% more than the cost price.
Statement IIThe selling price is Rs. 750.
ExplanationTogether: 750 = 1.25 × CP → CP = Rs. 600. Neither statement alone is sufficient.