A man buys 35 kg of sugar and sets a marked price in order to make a 20%…
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A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to
- A.
35
- B.
31
- C.
22
- D.
25
Attempted by 28 students.
Show answer & explanation
Correct answer: D
Let the cost price per kg be x.
The marked price is set to make a 20% profit, so marked price = 1.2x.
Revenue from 5 kg sold at the marked price = 5 × 1.2x = 6x.
Revenue from 15 kg sold at 10% discount on the marked price: per kg = 0.9 × 1.2x = 1.08x, so revenue = 15 × 1.08x = 16.2x.
3 kg are wasted, contributing 0 revenue. Remaining quantity = 35 − 5 − 15 − 3 = 12 kg.
For an overall profit of 15% on total cost 35x, total required revenue = 35x × 1.15 = 40.25x.
Revenue still needed from the remaining 12 kg = 40.25x − (6x + 16.2x) = 40.25x − 22.2x = 18.05x.
Required selling price per kg for the remaining 12 kg = 18.05x ÷ 12 ≈ 1.5041667x.
This final selling price is obtained by increasing the original marked price 1.2x by p%, so:
1.2x × (1 + p/100) = 1.5041667x
1 + p/100 = 1.5041667 ÷ 1.2 ≈ 1.2534722
p/100 ≈ 0.2534722, so p ≈ 25.34722%.
Answer: The required increase is approximately 25.35%, so the nearest given option is 25%.