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 Easy
An article is bought for Rs. 450 and sold for Rs. 495. What is the profit?
ExplanationProfit = SP − CP = 495 − 450 = Rs. 45. -
Q2 Easy
If the cost price is Rs. 800 and the selling price is Rs. 680, what is the loss?
ExplanationLoss = CP − SP = 800 − 680 = Rs. 120. -
Q3 Easy
A shopkeeper buys an item for Rs. 560 and sells it at a profit of 25%. What is the selling price?
ExplanationSP = CP × (100 + 25)/100 = 560 × 1.25 = Rs. 700. -
Q4 Medium
An article is sold for Rs. 920 at a profit of 15%. What is the cost price?
ExplanationCP = SP × 100/(100 + 15) = 920 × 100/115 = Rs. 800. -
Q5 Medium
An article is sold for Rs. 765 incurring a loss of 10%. Find the cost price.
ExplanationCP = SP × 100/(100 − 10) = 765 × 100/90 = Rs. 850. -
Q6 Easy
A trader sells an article at the same price at which he bought it. Which statement is correct?
ExplanationWhen CP = SP, profit and loss are both zero (break-even). -
Q7 Easy
The cost price of an article is Rs. 240 and the selling price is Rs. 300. What is the profit percentage?
ExplanationProfit = 60. Profit% = (60/240) × 100 = 25%.
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Q8 Medium
If the cost price is 80% of the selling price, what is the profit percentage on cost price?
ExplanationLet SP = 100, CP = 80. Profit% on CP = (20/80) × 100 = 25%. -
Q9 Medium
Two articles have cost prices Rs. 120 and Rs. 180. They are sold for Rs. 150 and Rs. 200 respectively. What is the total profit?
ExplanationProfits: 30 + 20 = Rs. 50. -
Q10 Easy
An article costing Rs. 750 is sold at a loss of 20%. What is the selling price?
ExplanationSP = 750 × 0.80 = Rs. 600. -
Q11 Medium
An article is sold for Rs. 1,150 at a profit of 15% on cost price. What is the profit amount?
ExplanationCP = 1150 × 100/115 = Rs. 1,000. Profit = Rs. 150. -
Q12 Medium
An article is bought for Rs. 625 and sold at a profit of 12%. What is the selling price?
ExplanationSP = 625 × 1.12 = Rs. 700. -
Q13 Hard
Two articles costing Rs. 500 and Rs. 700 are sold at 10% profit and 5% loss respectively. What is the overall profit or loss percentage on total cost price?
ExplanationTotal CP = Rs. 1,200, total SP = Rs. 1,215. Net profit Rs. 15 → 1.25% on CP. -
Q14 Hard
If 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, original SP = S. 2S − C = 3(S − C) → S = 2C. Original profit% = 100%.
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DS1 Easy
What is the cost price of the article?
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 SP. -
DS2 Medium
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.
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DS3 Medium
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 = 920. Statement II alone does not give SP without CP. -
DS4 Hard
What is the cost price of the article?
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.