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?
- (a) ₹ 28,000
- (b) ₹ 42,000 ✓ UPSC's answer
- (c) ₹ 56,000
- (d) ₹ 84,000
Why the answer is (b)
• Let the monthly incomes of X and Y be 4k and 3k respectively, based on the given ratio of 4:3.
• Let their monthly expenses be 3m and 2m respectively, based on the given ratio of 3:2.
• Since each saves ₹6,000, we form the equations: 4k - 3m = 6,000 and 3k - 2m = 6,000.
• Solving the second equation for m gives m = (3k - 6,000) / 2.
• Substituting this into the first equation: 4k - 3 * [(3k - 6,000) / 2] = 6,000.
• Simplifying yields 8k - 9k + 18,000 = 12,000, which leads to k = 6,000.
• The total monthly income is 4k + 3k = 7k = 7 * 6,000 = ₹42,000, matching option (b).
Why the other options are wrong
- (a) ₹ 28,000
- ₹28,000 is incorrect because it corresponds to a total income of 4k where k=7,000, which does not satisfy the savings condition of ₹6,000 for both individuals.
- (c) ₹ 56,000
- ₹56,000 is incorrect because it implies a total income of 7k where k=8,000, resulting in savings that do not equal ₹6,000 for both X and Y.
- (d) ₹ 84,000
- ₹84,000 is incorrect because it implies a total income of 7k where k=12,000, which results in savings significantly higher than ₹6,000 for both individuals.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.