Multiple choice

The ratio of the incomes of two persons is 9 : 7 and the respective ratio of their expenditures is 4 : 3. Each of them saves Rs. 2000 per month. Find their incomes.

  1. Rs. 14,000 and Rs. 18,000

  2. Rs. 16,000 and Rs. 18,000

  3. Rs. 18,000 and Rs. 14,000

  4. Rs. 10,000 and Rs. 16,000

  5. Rs. 18,000 and Rs. 16,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let incomes be 9x and 7x, and expenditures be 4y and 3y. We have 9x - 4y = 2000 and 7x - 3y = 2000. Solving this system: 27x - 12y = 6000 and 28x - 12y = 8000. Subtracting gives x = 2000. The incomes are 9(2000) = 18000 and 7(2000) = 14000.

AI explanation

Let the incomes of the two persons be 9x and 7x, and their expenditures be 4y and 3y. Using the savings formula, we establish 9x - 4y = 2000 and 7x - 3y = 2000. Multiplying the first equation by 3 and the second by 4 yields 27x - 12y = 6000 and 28x - 12y = 8000, and subtracting the first from the second gives x = 2000. Their incomes are 9 × 2000 = 18,000 and 7 × 2000 = 14,000.

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