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?
- (a) z < x < y ✓ UPSC's answer
- (b) x < y < z
- (c) y < x < z
- (d) z < y < x
Why the answer is (a)
• From the first condition, 0.7x + y = 1.65y, so 0.7x = 0.65y, giving x = (65/70)y = (13/14)y, which means x is less than y.
• From the second condition, 0.6x + z = 1.65z, so 0.6x = 0.65z, giving x = (65/60)z = (13/12)z, which means x is greater than z.
• Combining the two results, x < y and x > z, so the ordering is z < x < y.
• This corresponds to option (a).
Why the other options are wrong
- (b) x < y < z
- This claims x < y < z, but the second equation gives x = (13/12)z, meaning x > z, not x < z.
- (c) y < x < z
- This claims y < x < z, but the first equation gives x = (13/14)y, meaning x < y, not y < x.
- (d) z < y < x
- This claims z < y < x, but the first equation gives x = (13/14)y, meaning x < y, not y < x.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.