Mahesh buys 100 kg of rice for Rs. 1,040. He then sells the rice at such a rate that his loss in rupees is equal to the money he receives for 30 kg of rice. At what price per kilogram does he sell the rice?

Introduction / Context:
This question involves cost price per kilogram, selling price per kilogram and a condition that ties the total loss to the revenue from a specific quantity. Mahesh buys rice in bulk and sells it at a uniform rate per kilogram. The interesting twist is that his total loss equals the amount he earns from selling 30 kg of rice. This allows us to set up an equation relating total loss and selling price and solve for the selling price per kilogram.

Given Data / Assumptions:

• Total quantity of rice bought = 100 kg.
• Total cost price = Rs. 1,040.
• Therefore, cost price per kg is constant.
• He sells all rice at a single uniform selling price per kg, say x rupees.
• His total loss in rupees equals the money he receives for 30 kg of rice.
• We need to find the selling price per kg, x.

Concept / Approach:
First, we compute the cost price per kg by dividing total cost by total kilograms purchased. Let selling price per kg be x. Then total selling price for 100 kg is 100x. Loss equals total cost price minus total selling price. The condition states that this loss equals the revenue from 30 kg of rice, which is 30x. Therefore, we set total loss = 30x and solve the resulting equation for x.

Step-by-Step Solution:
Step 1: Total cost price = Rs. 1,040 for 100 kg. Step 2: Cost price per kg = 1,040 / 100 = Rs. 10.40. Step 3: Let selling price per kg = x rupees. Step 4: Total selling price for 100 kg = 100x rupees. Step 5: Total loss = total cost price - total selling price = 1,040 - 100x. Step 6: Given that loss equals the money received for 30 kg, so 1,040 - 100x = 30x. Step 7: Rearrange: 1,040 = 100x + 30x = 130x. Step 8: Therefore, x = 1,040 / 130. Step 9: Compute x: 1,040 / 130 = 8, so selling price per kg = Rs. 8.

Verification / Alternative check:
At Rs. 8 per kg, total selling price for 100 kg = 100 * 8 = Rs. 800. Total cost price = Rs. 1,040, so loss = 1,040 - 800 = Rs. 240. Money received for 30 kg at Rs. 8 per kg is 30 * 8 = Rs. 240. Thus, total loss equals the revenue from 30 kg, precisely matching the given condition.

Why Other Options Are Wrong:
If the selling price per kg were Rs. 7.46, Rs. 8.74, Rs. 8.56 or Rs. 7.80, the revenue from 30 kg would not equal the total loss when calculated with the same total cost of Rs. 1,040. For example, at Rs. 7.80, total SP for 100 kg is Rs. 780, loss is Rs. 260, but revenue on 30 kg is only Rs. 234, which does not match the loss.

Common Pitfalls:
A typical mistake is to equate the loss per kg to the price of 30 kg or to forget that the loss is computed on the entire 100 kg. Another error is to misinterpret the condition and set 100x - 1,040 = 30x instead of 1,040 - 100x = 30x. Carefully identifying that loss equals cost price minus selling price and that the loss is on the whole stock avoids these issues.

Final Answer:
Mahesh sells the rice at Rs. 8/kg.