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

The correct option is 25.

To find the value of $p$, we can break down the problem step-by-step by determining the total cost, the marked price, and the revenue generated from each part of the sale.

Step 1: Define the Cost Price (CP) and Marked Price (MP)
Let the Cost Price (CP) of 1 kg of sugar be $C$.
The man buys 35 kg of sugar, so the total Cost Price is:
$\text{Total CP}=35C$
He sets a marked price (MP) per kg to make a 20% profit. Therefore, the MP per kg is:
$\text{MP per kg}=1.2C$

Step 2: Calculate the Revenue from the Initial Sales
- First sale: He sells 5 kg at the marked price.
Revenue from this sale is:
${\text{Revenue}}_1=5\times 1.2C=6C$
- Second sale: He sells 15 kg at a 10% discount on the marked price.
The discounted price per kg is:
$1.2C\times (1-0.10)=1.08C$
Revenue from this sale is:
${\text{Revenue}}_2=15\times 1.08C=16.2C$

Step 3: Analyze the Remaining Sugar
- 3 kg of sugar is accidentally wasted, yielding 0 revenue.
- The total sugar sold or wasted so far is:
$5+15+3=23\text{kg}$
- The remaining quantity of sugar is:
$35-23=12\text{kg}$

Step 4: Calculate the Required Total Revenue for a 15% Overall Profit
To make an overall profit of 15% on the total cost price of 35 kg of sugar, the total revenue required is:
$\text{Total Revenue}=1.15\times 35C=40.25C$

Step 5: Determine the Price and Revenue for the Remaining Sugar
The revenue needed from the remaining 12 kg of sugar is the difference between the required total revenue and the revenue already earned:
${\text{Revenue}}_{\text{remaining}}=40.25C-(6C+16.2C)$
Simplifying this:
${\text{Revenue}}_{\text{remaining}}=40.25C-22.2C=18.05C$
Since this revenue is obtained by selling the remaining 12 kg, the selling price per kg for the remaining sugar is:
$\text{New Selling Price per kg}=\frac{18.05C}{12}\approx 1.5042C$

Step 6: Calculate the Percentage Increase $p$ in the Marked Price
The marked price is raised by $p$ percent to reach this new selling price. Thus, we have:
$1.2C\times (1+\frac{p}{100})=1.5042C$
Dividing both sides by $1.2C$:
$1+\frac{p}{100}=\frac{1.5042}{1.2}$
$1+\frac{p}{100}\approx 1.2535$
Subtracting 1 from both sides:
$\frac{p}{100}\approx 0.2535$
$p\approx 25.35$
Rounding to the nearest integer, we find:
$p\approx 25$