Multiple choice

A sum of Rs. 456 is divided among A, B and C such that A gets Rs. 120 more than B, and B gets Rs. 24 more than C. Find the ratio of shares of A, B and C.

  1. 10 : 5 : 4

  2. 12 : 9 : 8

  3. 20 : 10 : 9

  4. 5 : 4 : 2

  5. None of these
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A Correct answer
Explanation

Let C = x. Then B = x + 24, and A = (x + 24) + 120 = x + 144. Sum: x + x + 24 + x + 144 = 456 => 3x + 168 = 456 => 3x = 288 => x = 96. C = 96, B = 120, A = 240. Ratio A:B:C = 240:120:96 = 10:5:4.

AI explanation

Let B's share be x, which makes A's share (x + 120) and C's share (x - 24). The total sum gives the equation (x + 120) + x + (x - 24) = 456, which simplifies to 3x + 96 = 456, meaning 3x = 360 and x = 120. The shares of A, B, and C are 240, 120, and 96 respectively. Dividing all three values by their greatest common divisor of 24 gives the ratio 10 : 5 : 4. The required ratio is 10 : 5 : 4.

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