Sambhu buys rice at Rs. 10 per kilogram and sets a price that gives a 20 percent profit according to that marked rate. However, his weighing balance is faulty and shows 1000 grams when the true weight is only 800 grams. What is his actual gain percentage on the true cost of rice?

Introduction / Context:
This question combines the idea of profit based on marked price with an error in measurement. Sambhu thinks he is selling one kilogram, but due to a faulty balance he actually gives less rice while still charging the full selling price. This leads to an effective gain percentage that is higher than the marked profit because he is delivering reduced quantity for the same price.

Given Data / Assumptions:

• Cost price of rice is Rs. 10 per true kilogram.
• He marks the price to earn 20 percent profit.
• His balance shows 1000 grams when the actual weight is only 800 grams.
• We assume the marked price is applied on the visible one kilogram reading.
• We must find his actual gain percentage on the true cost.

Concept / Approach:
There are two sources of gain. First, he increases the price by 20 percent over the cost price. Second, he gives only 0.8 kilogram of rice when the customer believes they receive 1 kilogram. To compute the true gain, we consider the revenue from the sale corresponding to the price of one displayed kilogram and compare it with the real cost of the actual quantity delivered. The effective cost of 0.8 kilogram is lower than the cost of 1 kilogram, so the overall profit percentage increases.

Step-by-Step Solution:
True cost price per kilogram is 10 rupees.For a 20 percent profit, the marked selling price per kilogram equals 10 * 1.20 which is 12 rupees.Due to the faulty balance, when the scale shows 1000 grams, the customer actually receives only 800 grams.So for every indicated kilogram sold at 12 rupees, Sambhu gives 0.8 kilogram of rice.The true cost of 0.8 kilogram equals 0.8 * 10 which is 8 rupees.Therefore, profit per indicated kilogram sold equals 12 minus 8 which is 4 rupees.Percentage profit equals 4 divided by 8 multiplied by 100, which is 50 percent.

Verification / Alternative check:
Another way to see this is to compute effective selling price per true kilogram. Sambhu collects 12 rupees for 0.8 kilogram, so per true kilogram he effectively collects 12 divided by 0.8 which is 15 rupees. Comparing this with his cost price of 10 rupees per kilogram, the profit per kilogram is 5 rupees. The percentage profit is then 5 divided by 10 multiplied by 100 which is again 50 percent. Both methods agree on the same answer, so our calculations are consistent.

Why Other Options Are Wrong:
Option 25 percent would occur if he only had the marked price profit without any weighing error, which is not the case here. Option 75 percent and 60 percent are higher than the true calculated gain; they would require either a larger markup or an even bigger error in weight. The precise data given in the question leads to exactly 50 percent, making option 50 percent the only correct choice.

Common Pitfalls:
Some learners forget that the customer actually pays for an indicated kilogram but gets less rice, and they calculate profit using only the 20 percent markup. Others incorrectly treat 0.8 kilogram as 80 percent profit or mix up which quantity is treated as base in the percentage formula. Always identify the true cost of the actual quantity delivered and compare it with the amount collected from the customer to find the real gain percentage.

Final Answer:
Sambhu actual gain percentage on the transaction is 50 percent.