Multiple choice

The ratio of monthly income of A to that of B is 3 : 2 and their expenditures are in the respective ratio of 5 : 3. Each saves Rs. 1000 a month. Find the incomes of A and B.

  1. A - Rs. 6000, B - Rs. 4000

  2. A - Rs. 1500, B - Rs. 1000

  3. A - Rs. 3000, B - Rs. 2000

  4. A - Rs. 9000, B - Rs. 6000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let incomes be 3x and 2x, and expenditures be 5y and 3y. 3x - 5y = 1000 and 2x - 3y = 1000. Multiplying the first by 2 and second by 3: 6x - 10y = 2000 and 6x - 9y = 3000. Subtracting gives y = 1000. Then 3x - 5000 = 1000 => 3x = 6000 => x = 2000. Incomes are 3(2000) = 6000 and 2(2000) = 4000.

AI explanation

Let the incomes of A and B be 3x and 2x, and their expenditures be 5y and 3y respectively. Since each saves Rs. 1000, we have 3x - 5y = 1000 and 2x - 3y = 1000. Equating the two equations gives 3x - 5y = 2x - 3y, which simplifies to x = 2y. Substituting x = 2y into the second equation gives 4y - 3y = 1000, so y = 1000 and x = 2000. The income of A is 3x = Rs. 6000 and the income of B is 2x = Rs. 4000.

Keep practicing — related questions