If rice is sold at Rs. 56 per kilogram, the shopkeeper incurs a loss of 40% on the cost price. To earn a profit of 20% instead, at what price per kilogram should he sell the rice?

Introduction / Context:
This question explores how the selling price of a commodity affects whether the seller incurs a loss or gains a profit. Initially, selling rice at a given price leads to a 40% loss. We are then asked to find the new selling price that would instead yield a 20% profit on the same cost price. It is a classic example of working with loss and profit percentages to find correct selling prices in aptitude exams.

Given Data / Assumptions:

• When sold at Rs. 56 per kg, there is a loss of 40%.
• Let the cost price (CP) per kg be C.
• Loss of 40% means selling price SP1 = 0.60C = Rs. 56.
• We want a profit of 20%, so desired selling price SP2 = 1.20C.
• We must find SP2 in rupees per kilogram.

Concept / Approach:
First, we determine the cost price from the loss scenario. A 40% loss implies that selling price is 60% of cost price. From SP1 = 0.60C = 56, we solve for C. Once C is known, calculating the selling price for a 20% profit is straightforward using SP2 = 1.20C. This stepwise approach keeps the logic clear and avoids confusion between loss and profit percentages.

Step-by-Step Solution:
Let cost price per kg be C rupees. A loss of 40% means selling price SP1 = 60% of CP = 0.60C. We are told SP1 = Rs. 56. So, 0.60C = 56. Therefore, C = 56 / 0.60. 56 / 0.60 = 56 * (100 / 60) / 100 = 5600 / 60 = 280 / 3 ≈ 93.33. Now we want a profit of 20%, so new selling price SP2 = 1.20C. SP2 = 1.20 * (280 / 3). 1.20 = 6 / 5, so SP2 = (6 / 5) * (280 / 3) = (6 * 280) / (15). 6 * 280 = 1,680. So SP2 = 1,680 / 15 = 112. Hence, the new selling price should be Rs. 112 per kg.

Verification / Alternative check:
Using C = 280 / 3 ≈ 93.33, selling at Rs. 56 gives loss = 93.33 − 56 ≈ 37.33. Loss percentage ≈ (37.33 / 93.33) * 100 ≈ 40%, confirming the first condition. At the new selling price Rs. 112, profit = 112 − 93.33 ≈ 18.67. Profit percentage ≈ (18.67 / 93.33) * 100 ≈ 20%, confirming the second condition.

Why Other Options Are Wrong:
108 and 116: These are close values but when checked, they do not yield exactly 20% profit on the calculated cost price.
124: This gives a profit greater than 20% and does not satisfy the condition exactly.
96: This price is only slightly above the cost price and corresponds to a much smaller profit percentage.

Common Pitfalls:
A frequent error is to directly add 40% and 20%, mistakenly thinking the new price is some simple percentage of the old selling price. Another mistake is to compute cost price incorrectly by treating 56 as 40% of C instead of 60%. The correct interpretation is that after a 40% loss, the seller receives only 60% of the cost price as selling price. Getting this relationship right is crucial.

Final Answer:
To earn a 20% profit, the shopkeeper should sell the rice at Rs. 112 per kilogram.