Question:hard

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

Updated On: Jan 15, 2026
  • 31
  • 22
  • 35
  • 25
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The Correct Option is D

Solution and Explanation

To address the problem, we first establish that the objective is to achieve a 15% total profit on 35 kg of sugar. The cost price (CP) for the entire quantity is calculated assuming a CP of $1 per kg, resulting in a total CP of $35.

The initial intent is to mark up the price by 20% to achieve a profit. The marked price (MP) per kg is determined as follows:

MP = CP × (1 + Profit%) = $1 × (1 + 0.20) = $1.20

The sales distribution proceeds as follows:

  • Sale 1: 5 kg are sold at the MP, generating a revenue of 5 × $1.20 = $6.
  • Sale 2: 15 kg are sold with a 10% discount on the MP:

The discounted price per kg is $1.20 × (1 - 0.10) = $1.08. The total revenue from this sale is 15 × $1.08 = $16.20.

  • The remaining sugar quantity is 35 kg - 5 kg - 15 kg - 3 kg (wasted) = 12 kg.

A total profit of 15% is targeted on the initial investment of $35. Therefore, the required selling price (RSP) for all the sugar must be:

RSP = CP × (1 + Overall Profit%) = $35 × 1.15 = $40.25

The revenue generated from the first two sales amounts to $6 + $16.20 = $22.20.

To achieve the targeted overall profit of 15%, the remaining revenue needed from the 12 kg of sugar is:

Required additional revenue = $40.25 - $22.20 = $18.05

Consequently, the selling price per kg for the remaining sugar must be $18.05 / 12 = $1.504.

To ascertain the percentage increase (p%) above the original MP ($1.20), we use the formula:

New price = MP × (1 + p/100)

Substituting the values: $1.504 = $1.20 × (1 + p/100).

Solving for p:

1 + p/100 = 1.504 / 1.20 = 1.25333

p/100 = 1.25333 - 1 = 0.25333

p = 0.25333 × 100 = 25.333%. Rounded to the nearest integer, p is 25%.

Therefore, p is closest to 25.

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