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, which simplifies to 0.7x = 0.65y, giving the ratio x/y = 65/70 = 13/14, so x < y.

• From the second condition, 0.6x + z = 1.65z, which simplifies to 0.6x = 1.05z, giving the ratio x/z = 105/60 = 7/4, so x > z.

• Combining these two inequalities, we get z < x < y.

• Therefore, the correct relationship is z < x < y, which corresponds to option (a).

Why the other options are wrong

(b) x < y < z: This option incorrectly states x < y < z, but the calculation shows x > z.
(c) y < x < z: This option incorrectly states y < x < z, but the calculation shows x < y and x > z.
(d) z < y < x: This option incorrectly states z < y < x, but the calculation shows x < y.

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.