UPSC Prelims 2017 · CSAT
Question 74: Basic Numeracy
The monthly incomes of X and Y are in the ratio of 4 : 3 and their monthly expenses are in the ratio of 3 : 2. However, each saves ₹ 6,000 per month. What is their total monthly income?
AnswerUPSC’s answer is (b).
Let incomes be 4x and 3x and expenses 3y and 2y. Each saves 6000, so 4x - 3y = 6000 and 3x - 2y = 6000. Multiply the first by 2 and the second by 3: 8x - 6y = 12000 and 9x - 6y = 18000. Subtracting gives x = 6000. Incomes are 24000 and 18000, so the total is ₹42,000 (expenses of 18000 and 12000 confirm the savings).
Why each option is right or wrong
- (a) ₹28,000 would need x = 4000, which fails the equations.
- (b) Correct: 24,000 + 18,000 = ₹42,000.
- (c) ₹56,000 implies x = 8000, which fails.
- (d) ₹84,000 implies x = 12000, which fails.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2017, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.