Profit and Loss – Price gain plus 30% short measure: A man sells rice at a 10% profit but uses weights that are 30% less than the correct measure. What is his overall gain percentage on the true quantity delivered?

Introduction / Context:
This problem combines a declared price gain with a quantity shortfall. The effective revenue per true kilogram rises due to both the higher price and the reduction in the amount delivered for each labeled kilogram. Multiplying the factors gives the exact overall gain.

Given Data / Assumptions:

• Price gain = 10% ⇒ factor 1.10
• Weight used = 70% of true (30% short) ⇒ customer gets 0.70 kg while paying for 1 kg

Concept / Approach:
Short measure factor = 1 / 0.70 = 10/7. Overall multiplier = 1.10 * (10/7). The net gain% is (overall − 1) * 100. Express the result as a mixed fraction for clarity.

Step-by-Step Solution:
Overall factor = 1.10 * (10/7) = 11/7 ≈ 1.571428...Gain% = (11/7 − 1) * 100 = (4/7) * 100 = 400/7% ≈ 57.142% = 57 1/7%

Verification / Alternative check:
Try CP = ₹ 7 per true kg. With 10% price gain and 0.70 kg delivered per labeled kg, revenue per true kg becomes ₹ 11, which is 57.142% above ₹ 7.

Why Other Options Are Wrong:
The other fractional forms approximate different values around 57%, but only 57 1/7% matches the exact 400/7%.

Common Pitfalls:
Adding 10% and 30% to get 40%—incorrect because one is price-based and the other is quantity-based, which multiply.

Final Answer:
57 1/7% (≈57.142%)