UPSC Prelims 2016 CSAT Paper II · Q37 of 79 Basic Numeracy easy

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 ?

  1. (a) 12%
  2. (b) 10% ✓ UPSC's answer
  3. (c) 9%
  4. (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.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

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