UPSC Prelims 2015 · CSAT
Question 70: Basic Numeracy
The monthly incomes of Peter and Paul are in the ratio of 4 : 3. Their expenses are in the ratio of 3 : 2. If each saves ₹ 6,000 at the end of the month, their monthly incomes respectively are (in ₹)
AnswerUPSC’s answer is (a).
Let incomes be 4x and 3x and expenses 3y and 2y. Saving is income minus expense: 4x − 3y = 6000 and 3x − 2y = 6000. Multiply the first by 2 and the second by 3: 8x − 6y = 12000 and 9x − 6y = 18000. Subtract: x = 6000. Incomes are 24,000 and 18,000. Check: expenses are 18,000 and 12,000, both leaving 6,000.
Why each option is right or wrong
- (a) Right: x = 6000 gives 24,000 and 18,000.
- (b) Wrong: 28,000 and 21,000 leave expenses of 22,000 and 15,000, a ratio of 22 : 15, not 3 : 2.
- (c) Wrong: 32,000 and 24,000 leave expenses of 26,000 and 18,000, a ratio of 13 : 9, not 3 : 2.
- (d) Wrong: 34,000 and 26,000 leave expenses of 28,000 and 20,000, a ratio of 7 : 5, not 3 : 2.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2015, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.