Multiple choice

DIRECTION for the question: Solve the following question and mark the best possible option. Rs. 8400 is divided among A, B, C, and D in such a way that the shares of A and B, B and C as well as C and D are in the ratios of 2:3, 4:5, and 6:7 respectively. What will be the share of A?

  1. 1280

  2. 1320

  3. 8210

  4. 8400

  5. 4200
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A Correct answer
Explanation

A:B = 2:3, B:C = 4:5, C:D = 6:7. Normalize ratios: A:B = 16:24, B:C = 24:30, C:D = 30:35. A:B:C:D = 16:24:30:35. Sum = 105 parts. A's share = (16/105) * 8400 = 16 * 80 = 1280.

AI explanation

To combine the ratios, express B as the least common multiple of its values in the first two ratios, which is 12. The ratio A:B becomes 8:12, the ratio B:C becomes 12:15, and multiplying C:D by 5 makes it 15:17.5. The combined ratio of A:B:C:D is 8:12:15:17.5, which is multiplied by 2 to remove the decimal, resulting in 16:24:30:35. The sum of the ratio units is 105, and A's share is calculated as 8400 multiplied by 16 and divided by 105, which gives Rs. 1280.

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