The Problem

A farmer sells one quintal of rice for Rs. 964 and earns a profit of 12 percent. However, when the farmer sells one quintal of wheat for the same amount, he incurs a loss of 12 percent. We need to find the cost price of both rice and wheat.

Solution

Let's assume the cost price of one quintal of rice is 'x' rupees.

Profit on Rice

We know that the farmer earns a profit of 12 percent on the sale of rice. Therefore, the selling price of rice would be the cost price plus the profit.

Selling Price of Rice = Cost Price of Rice + Profit
964 = x + 12% of x

To calculate 12% of x, we multiply x by 12% (0.12):

964 = x + 0.12x
964 = 1.12x

Now, we can solve the equation to find the value of x:

x = 964 / 1.12
x ≈ 861.07

Therefore, the cost price of one quintal of rice is approximately Rs. 861.07.

Loss on Wheat

Similarly, let's assume the cost price of one quintal of wheat is 'y' rupees.

Loss on Wheat

We know that the farmer incurs a loss of 12 percent on the sale of wheat. Therefore, the selling price of wheat would be the cost price minus the loss.

Selling Price of Wheat = Cost Price of Wheat - Loss
964 = y - 12% of y

To calculate 12% of y, we multiply y by 12% (0.12):

964 = y - 0.12y
964 = 0.88y

Now, we can solve the equation to find the value of y:

y = 964 / 0.88
y ≈ 1095.45

Therefore, the cost price of one quintal of wheat is approximately Rs. 1095.45.

Summary

- The cost price of one quintal of rice is approximately Rs. 861.07.
- The cost price of one quintal of wheat is approximately Rs. 1095.45.

Thus, we have found the cost prices of both rice and wheat based on the given information.