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 ₹)
- (a) 24,000 and 18,000 ✓ UPSC's answer
- (b) 28,000 and 21,000
- (c) 32,000 and 24,000
- (d) 34,000 and 26,000
Why the answer is (a)
• Let the monthly incomes of Peter and Paul be 4x and 3x respectively, based on the given ratio of 4:3.
• Let their monthly expenses be 3y and 2y respectively, based on the given ratio of 3:2.
• Since each saves ₹6,000, we form the equations: 4x - 3y = 6,000 and 3x - 2y = 6,000.
• To eliminate y, multiply the first equation by 2 and the second by 3, resulting in 8x - 6y = 12,000 and 9x - 6y = 18,000.
• Subtracting the first modified equation from the second gives x = 6,000.
• Substituting x = 6,000 back into the income expressions yields Peter's income as 4(6,000) = 24,000 and Paul's income as 3(6,000) = 18,000, which matches option (a).
Why the other options are wrong
- (b) 28,000 and 21,000
- With incomes of 28,000 and 21,000, equal savings giving a 3 : 2 expense ratio would be ₹ 7,000, not ₹ 6,000.
- (c) 32,000 and 24,000
- With incomes of 32,000 and 24,000, equal savings giving a 3 : 2 expense ratio would be ₹ 8,000, not ₹ 6,000.
- (d) 34,000 and 26,000
- The incomes 34,000 and 26,000 do not maintain the required 4:3 income ratio (34:26 simplifies to 17:13).
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.