Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X ?
- (a) 12%
- (b) 10% ✓ UPSC's answer
- (c) 9%
- (d) 8%
Why the answer is (b)
• Let the third number Z be 100 for ease of calculation.
• Since X is 20% less than Z, X = 100 - 20 = 80.
• Since Y is 28% less than Z, Y = 100 - 28 = 72.
• The difference between X and Y is 80 - 72 = 8.
• To find by what percentage Y is less than X, divide the difference by X: (8 / 80) * 100 = 10%.
• Therefore, Y is 10% less than X, which corresponds to option (b).
Why the other options are wrong
- (a) 12%
- 12% is the difference in the percentages relative to Z, not the percentage difference relative to X.
- (c) 9%
- 9% is an incorrect calculation that does not follow from the given values of X and Y.
- (d) 8%
- 8% is the absolute difference between X and Y, not the percentage difference relative to X.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.