UPSC Prelims 2022 · CSAT
Question 60: Basic Numeracy
When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. Which one of the following is correct?
AnswerUPSC’s answer is (a).
From the first condition: 0.7x + y = 1.65y, so 0.7x = 0.65y and y = (0.7/0.65)x ≈ 1.077x, hence y > x. From the second: 0.6x + z = 1.65z, so 0.6x = 0.65z and z = (0.6/0.65)x ≈ 0.923x, hence z < x. So z < x < y (taking x positive). In words, 70% of x equals 65% of y, so y is bigger than x; 60% of x equals 65% of z, so z is smaller than x.
Why each option is right or wrong
- (a) Correct: z ≈ 0.92x and y ≈ 1.08x, so z < x < y.
- (b) x < y < z puts z above x, but z < x.
- (c) y < x < z puts y below x, but y > x.
- (d) z < y < x puts y below x, but y > x.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.