Multiple choice

A sum (in Rs.) is distributed between A, B and C in the ratio 9 : 6 : 11. If A gives Rs. 500 from his share to C, the ratio of shares of A, B and C becomes 4 : 3 : 6. What is the sum of shares (in Rs.) of B and C in the beginning?

  1. Rs. 8,500

  2. Rs. 9,100

  3. Rs. 7,800

  4. Rs. 7,500
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A Correct answer
Explanation

Initial shares: 9x, 6x, 11x. After A gives 500: (9x-500)/6x/11x+500 = 4/3/6. Solving (9x-500)/6x = 4/3 gives 27x - 1500 = 24x, so 3x = 1500, x = 500. B+C = 6x + 11x = 17x = 17 * 500 = 8500.

AI explanation

Let the initial shares of A, B, and C be 9x, 6x, and 11x. After A gives Rs. 500 to C, their new shares become 9x - 500 and 11x + 500, making the new ratio of A to C equal to 4 : 6. Setting up the proportion (9x - 500) / (11x + 500) = 4 / 6 and cross-multiplying gives 54x - 3000 = 44x + 2000, which simplifies to 10x = 5000 and x = 500. The initial sum of the shares of B and C is 6x + 11x, or 17x, so 17 multiplied by 500 gives Rs. 8500. The sum is Rs. 8500.

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