A shopkeeper marked a watch at ₹800. He sold it after allowing a 15% discount. If his profit on the sale was 20%, what was the cost price of the watch?
- (a)₹542.36
- (b)₹536.47
- (c)₹566.67
- (d)₹596.34
Answer
Why
Correct — C. Find the selling price from the discount, then undo the profit.
Discount: 15% of 800 = 120
Selling price: 800 − 120 = ₹680
Profit 20% means SP = 1.2 × CP
CP = 680 ÷ 1.2 = 566.666…
Rounded to two decimals: ₹566.67 → option (c)
Why the others are wrong
- (a)₹542.36 — At a cost of ₹542.36, selling at ₹680 earns ₹137.64, a profit of about 25.4%, not 20%.
- (b)₹536.47 — A cost of ₹536.47 makes the profit 680 − 536.47 = ₹143.53, about 26.8% of cost, well above the stated 20%.
- (d)₹596.34 — A cost of ₹596.34 leaves a profit of ₹83.66 on the ₹680 sale, about 14%, short of 20%.
Concept
Three prices run in a chain: marked price → selling price → cost price.
The discount is a percentage of the marked price: SP = 800 × (1 − 15⁄100) = 800 × 0.85 = 680.
The profit is a percentage of the cost price, not of SP: SP = CP × (1 + 20⁄100). So you divide by 1.2 to go back. Taking 20% off 680 gives ₹544, which is wrong.
680 ÷ 1.2 = 1700⁄3 = 566.666…, a recurring decimal, so the key prints it as ₹566.67.
Key facts
- Discount is a percentage of the marked price.
- Profit percentage is a percentage of the cost price.
- CP = SP ÷ (1 + profit% ⁄ 100), so CP = 680 ÷ 1.2 here.
Study next
Common traps
- Taking 20% off the selling price, 680 × 0.8 = ₹544, instead of dividing by 1.2.
- Applying the 15% discount to the cost price rather than the marked price.
17 Sep 2025, 16:00, Quant Q.4 runs the chain forward, from marked price and discount to a loss percentage. 21 Sep 2025, 16:00, Quant Q.13 runs it backward to a cost price of Rs. 333.33, another recurring decimal printed to two places.
Related PYQs
No directly related past PYQ was found.