Jatin buys an article for 10% less than its value and sells it for 10% more…
20172021
Jatin buys an article for 10% less than its value and sells it for 10% more than its value. His gain is:
- A.
20%
- D.
None of the above
Show answer & explanation
Gain percentage is always calculated on the Cost Price (CP): Gain% = (SP − CP) / CP × 100. When the cost price and selling price are both defined as percentage adjustments to some other reference value (here, the article's “value”), first convert both to actual amounts in terms of that reference, and then compute the gain purely from CP and SP — never divide the gain by the reference value itself.
Let the article's actual value be Rs. 100.
Cost Price (CP) = value − 10% of value = 100 − 10 = Rs. 90 (Jatin buys 10% below value).
Selling Price (SP) = value + 10% of value = 100 + 10 = Rs. 110 (Jatin sells 10% above value).
Gain = SP − CP = 110 − 90 = Rs. 20.
Gain% = (Gain / CP) × 100 = (2090) × 100 = 2009% = 22 29%.
Independent check with a general formula: if the cost price is x% less than a base value and the selling price is y% more than that same base value, the gain percentage on the cost price is (x + y) / (100 − x) × 100.
Substituting x = y = 10: (10 + 10) / (100 − 10) × 100 = 2090 × 100 = 2009% = 22 29%, the same result as above — directly ruling out 20% (which comes from simply adding the two percentage changes) and 22 79% (an arithmetic slip in reducing the fraction).