A seller offers a 40% discount on an item whose cost price is Rs. 720. Despite the discount, the seller earns a profit of 20%. What must be the marked price?
- (a)Rs. 1,600
- (b)Rs. 1,240
- (c)Rs. 1,500
- (d)Rs. 1,440
Answer
Why
Correct — D. Get the selling price from the profit, then the marked price from the discount.
Selling price = 720 × 1.20 = Rs. 864
A 40% discount means the buyer pays 60% of the marked price
Marked price = 864 ÷ 0.60 = Rs. 1,440 → option (d).
Check: 40% of 1,440 = 576, and 1,440 − 576 = 864.
Why the others are wrong
- (a)Rs. 1,600 — Rs. 1,600 less 40% is Rs. 960, a profit of 240 on 720. That is 33.3%, not the 20% the seller earns.
- (b)Rs. 1,240 — Rs. 1,240 less 40% is Rs. 744, just 24 above the cost of 720. That is a profit of about 3.3%, not 20%.
- (c)Rs. 1,500 — Rs. 1,500 less 40% is Rs. 900, a profit of 180 on 720. That is 25%, five points above the stated 20%.
Concept
Three prices sit in a chain: cost price → selling price → marked price. Profit % links the first two and is taken on the cost price. Discount % links the last two and is taken on the marked price.
Work outward from the price you know. Here SP = 1.2 × CP and SP = 0.6 × MP, so MP = CP × 1.2 ÷ 0.6 = 2 × CP = 1,440.
Key facts
- Profit % is calculated on the cost price.
- Discount % is calculated on the marked price.
- MP = CP × (100 + profit %) ÷ (100 − discount %) = 720 × 120 ÷ 60 = 1,440.
Study next
Common traps
- Adding the two percentages and marking 720 up by 60% to get 1,152.
- Taking the 40% discount on the cost price instead of on the marked price.
The same chain run backwards, from marked price to cost price, is 18 Sep 2025, 09:00, Quant Q.5: ₹800 less 15% is ₹680, and a 20% profit puts the cost at 680 ÷ 1.2 = ₹566.67.
24 Sep 2025, 12:30, Quant Q.12 runs it from a selling price: Rs. 120 after the discount with a 20% profit gives a cost of Rs. 100.
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