How many kilograms of wheat costing Rs.8 per kg must be mixed with 36 kg of rice costing Rs.5.40 per kg so that 20% gain may be obtained by selling the mixture at Rs.7.20 per kg?Options :10 kg10.2 kg10.6 kg10.8 kg

To solve this problem, we need to find the quantity of wheat that should be mixed with the rice.

Let's denote the quantity of wheat to be mixed as 'x' kg.

Given:

• Cost of wheat = Rs.8 per kg
• Cost of rice = Rs.5.40 per kg for 36 kg = Rs.194.40
• Selling price of the mixture = Rs.7.20 per kg
• Gain = 20%

First, we need to find the cost price of the mixture. Since a gain of 20% is obtained from selling the mixture, the cost price of the mixture per kg would be 100/120 * 7.20 = Rs.6 per kg.

The total cost price of the mixture would be Rs.6 * (x + 36) = 6x + 216.

This total cost price of the mixture should be equal to the sum of the cost of the wheat and the cost of the rice. So, we have the equation:

8x (cost of wheat) + 194.40 (cost of rice) = 6x (cost of mixture) + 216

Solving this equation for 'x' gives us:

8x - 6x = 216 - 194.40 2x = 21.60 x = 21.60 / 2 x = 10.8

So, 10.8 kg of wheat should be mixed with the 36 kg of rice. The correct option is 10.8 kg.

Let's denote the amount of wheat to be mixed as 'x' kg.

The cost price of the wheat is Rs.8 per kg, so the total cost of the wheat is 8x.

The cost price of the rice is Rs.5.40 per kg, so the total cost of the rice is 5.40 * 36 = Rs.194.40.

The total cost of the mixture is therefore 8x + 194.40.

We want to sell the mixture at Rs.7.20 per kg and make a 20% gain.

This means the selling price of the mixture is 120% of the total cost, or 1.2 * (8x + 194.40).

The total weight of the mixture is x + 36 kg, so the selling price per kg is 1.2 * (8x + 194.40) / (x + 36).

We set this equal to Rs.7.20 and solve for x:

7.20 = 1.2 * (8x + 194.40) / (x + 36)

Solving this equation gives x = 10.8 kg.

So, 10.8 kg of wheat must be mixed with the rice.

Therefore, the correct option is 10.8 kg.