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Select the correct answerThe income of A, B, and C are in the ratio 3 : 4 : 7. If their incomes be changed such that the new income of A is 50% increased, 25% increased for B and 25% decrease for C. Find the ratio of their new incomes.Options17 : 12 : 2118 : 40 : 2318 : 20 : 2128 : 20 : 21

Question

Select the correct answerThe income of A, B, and C are in the ratio 3 : 4 : 7. If their incomes be changed such that the new income of A is 50% increased, 25% increased for B and 25% decrease for C. Find the ratio of their new incomes.Options17 : 12 : 2118 : 40 : 2318 : 20 : 2128 : 20 : 21

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Solution

Let's solve this step by step:

  1. Let's assume the initial incomes of A, B, and C to be 3x, 4x, and 7x respectively.

  2. According to the problem, the new income of A is increased by 50%. So, the new income of A = 3x + 50% of 3x = 3x + 1.5x = 4.5x.

  3. The new income of B is increased by 25%. So, the new income of B = 4x + 25% of 4x = 4x + x = 5x.

  4. The new income of C is decreased by 25%. So, the new income of C = 7x - 25% of 7x = 7x - 1.75x = 5.25x.

  5. Therefore, the new ratio of their incomes = 4.5x : 5x : 5.25x.

  6. To simplify this ratio, we can multiply all terms by 4 to get rid of the decimal, which gives us 18x : 20x : 21x.

  7. Since 'x' is common to all terms, we can remove it to get the final ratio 18 : 20 : 21.

So, the correct answer is 18 : 20 : 21.

This problem has been solved

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