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?
Answer & explanation
Answer: (a) z < x < y
The first condition gives 0.7x = 0.65y, so y = 14x/13, just above x. The second gives 0.6x = 0.65z, so z = 12x/13, just below x. Hence z < x < y.
- 0.7x + y = 1.65y, so 0.7x = 0.65y and y = 70x/65 = 14x/13.
- 0.6x + z = 1.65z, so 0.6x = 0.65z and z = 60x/65 = 12x/13.
- For positive x, 12x/13 < x < 14x/13, so z < x < y.
- Check with x = 13: y = 14 and z = 12; 9.1 + 14 = 23.1 = 1.65 × 14 and 7.8 + 12 = 19.8 = 1.65 × 12.
Remember · Turn each percentage condition into ‘part of x = part of y’ and compare the resulting multiples of x.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·