An article listed at Rs 3600 is sold to a retailer at a successive discount of…
2024
An article listed at Rs 3600 is sold to a retailer at a successive discount of 30% and 20%. The retailer desires a profit of 25%, after allowing a discount of 10% to the customer. At what price should he list the article (in Rs.)?
- A.
Rs. 2680
- B.
Rs. 2700
- C.
Rs. 2800
- D.
Rs. 2760
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Correct answer: C
Concept: When an item passes through successive percentage discounts, the resulting price is found by multiplying by (1 − discount) for each stage in turn, not by adding the discounts together. Separately, a desired profit percentage is always applied on the cost price (Selling Price = Cost Price × (1 + profit%)), and when a further discount is offered to the end customer, the required marked/listed price is recovered by dividing the target selling price by (1 − discount%), since Selling Price = Listed Price × (1 − discount%).
Find the retailer's cost price after both successive discounts on the original list price: Cost Price = 3600 × (1 − 0.30) × (1 − 0.20) = 3600 × 0.7 × 0.8 = Rs. 2016.
Find the selling price the retailer needs to earn a 25% profit on this cost: Selling Price = 2016 × (1 + 0.25) = 2016 × 1.25 = Rs. 2520.
Since this selling price is reached only after a 10% discount off the new listed price, recover the listed price: Listed Price × (1 − 0.10) = 2520, so Listed Price = 2520 ÷ 0.90 = Rs. 2800.
Check: Rs. 2800 discounted by 10% gives 2800 × 0.90 = Rs. 2520, and Rs. 2520 is exactly 25% more than the cost price of Rs. 2016 (2016 × 1.25 = 2520), confirming the listed price.