A merchant has 1000 kg of sugar, part of which he sells at a 10% profit and the rest at a 40% profit. He gains 20% on the whole. The quantity sold at 40% profit is:

Correct option is C

Given:

Quantity of sugar = 1000 kg

Initial profit = 10%

Profit on rest = 40%

Profit on the whole quantity = 20%

Formula Used:

SP = $$\frac{100+Profit\%}{100}\times CP$$​​

Solution:

A merchant has 1000 kg of sugar, part of which he sells at a 10% profit and the rest at a 40% profit.

He gains 20% on the whole. We need to find the quantity sold at a 40% profit.

Let the quantity sold at 40% profit be x kg.

Then, the quantity sold at 10% profit is (1000 - x) kg.

The total cost price of 1000 kg of sugar = 1000 ×C (where C is the cost price per kg).

The total profit from selling x kg at 40% profit is: 0.40 ×x × C.

The total profit from selling (1000 - x) kg at 10% profit is: 0.10 × (1000 - x) × C.

The total profit from the whole sugar is: 0.20 × 1000 ×C.

Thus, the total profit equation becomes:

0.40 × x × C + 0.10 × (1000 - x) × C = 0.20 × 1000 × C

Dividing the equation by C:

0.40 × x + 0.10 × (1000 - x) = 200

Expanding:

0.40 × x + 100 - 0.10 × x = 200

Simplifying:

0.30 × x + 100 = 200

0.30 × x = 100

x = 100 / 0.30

​$$x = 333\frac{1}{3} kg$$​​

The quantity sold at 40% profit is approximately 333.33 kg.