UPSC Prelims 2010 · General Studies

Question 53: Basic Numeracy

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 ?

a8%

b9%

c10%

d12%

AnswerThe answer is (c).

Take Z = 100. X is 20 per cent less, so X = 80. Y is 28 per cent less, so Y = 72. Y is less than X by 80 - 72 = 8, and as a percentage of X that is 8 / 80 x 100 = 10 per cent. Remember: a percentage difference is taken on the number you compare against (here X), not on Z; 8 per cent is the mistake of using Z.

Why each option is right or wrong

(a) 8% is the gap as a share of Z, not of X.
(b) 9% has no basis in the working.
(c) Right: 8 out of 80 is 10 per cent.
(d) 12% has no basis in the working.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2010, General Studies, Series A. The paper on upsc.gov.in.