Multiple choice

The monthly incomes of Vasu and Ravi are in the ratio 7 : 8 and their monthly expenditures are in the ratio 3 : 4, respectively. If the respective savings of Vasu and Ravi are Rs. 2,400 and Rs. 1,600, then find the monthly income of Ravi.

  1. Rs. 9,600

  2. Rs. 8,400

  3. Rs. 7,200

  4. Rs. 6,500

  5. None of these
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A Correct answer
Explanation

Let incomes be 7x and 8x. Expenditures are 3y and 4y. Savings: 7x - 3y = 2400 and 8x - 4y = 1600. Solving this system: 4y = 8x - 1600, so y = 2x - 400. Substitute into the first: 7x - 3(2x - 400) = 2400, 7x - 6x + 1200 = 2400, x = 1200. Ravi's income is 8x = 9600.

AI explanation

Let the monthly incomes of Vasu and Ravi be 7x and 8x, and let their monthly expenditures be 3y and 4y. Their savings give the equations 7x - 3y = 2400 and 8x - 4y = 1600. Multiplying the first equation by 4 and the second by 3, and then subtracting, eliminates y and yields 4x = 4800, so x = 1200. Therefore, the monthly income of Ravi is 8x = 8 x 1200 = Rs. 9,600.

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