The 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.Options28 : 20 : 2117 : 12 : 2118 : 40 : 2318 : 20 : 21
Question
The 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.Options28 : 20 : 2117 : 12 : 2118 : 40 : 2318 : 20 : 21
Solution
Let's solve this step by step:
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Let's assume the initial incomes of A, B, and C to be 3x, 4x, and 7x respectively.
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According to the problem, A's income is increased by 50%. So, the new income of A = 3x + 50% of 3x = 3x + 1.5x = 4.5x.
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B's income is increased by 25%. So, the new income of B = 4x + 25% of 4x = 4x + x = 5x.
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C's income is decreased by 25%. So, the new income of C = 7x - 25% of 7x = 7x - 1.75x = 5.25x.
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Therefore, the new ratio of their incomes = 4.5x : 5x : 5.25x.
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To simplify this, we can multiply the entire ratio by 4 to get rid of the decimal, which gives us 18x : 20x : 21x.
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Since 'x' is common in all, we can remove it. So, the new ratio of their incomes is 18 : 20 : 21.
So, the correct option is 18 : 20 : 21.
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