UPSC Prelims 2017·CSAT·Quantitative Aptitude·Arithmetic

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 Rs. 6,000 per month. What is their total monthly income?

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Last updated 8 Jul 2026, 4:39 pm IST
  1. ARs. 28,000
  2. BRs. 42,000Correct
  3. CRs. 56,000
  4. DRs. 84,000

Explanation

Let X's income be 4k and Y's income be 3k. Let X's expense be 3m and Y's expense be 2m.

Since Income - Expense = Savings, we can set up two equations:

  1. For X: 4k - 3m = 6000
  2. For Y: 3k - 2m = 6000

To solve for k, we can eliminate m. Multiply equation (1) by 2: 8k - 6m = 12000 Multiply equation (2) by 3: 9k - 6m = 18000

Subtract the first modified equation from the second modified equation: (9k - 6m) - (8k - 6m) = 18000 - 12000 9k - 8k = 6000 k = 6000

The total monthly income is the sum of X's and Y's incomes: Total income = 4k + 3k = 7k Total income = 7 * 6000 = Rs. 42,000

Therefore, option B is correct.

Analysis of options: A) Rs. 28,000: This would be X's income (4k) if k=7000, or 7k if k=4000. Incorrect. B) Rs. 42,000: This matches our calculated total income (7k where k=6000). Correct. C) Rs. 56,000: This would be 8k. Incorrect. D) Rs. 84,000: This would be 12k. Incorrect.

Quantitative Aptitude: 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
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