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correct answerTotal income of A, B and C is 6060 and they spend 80%, 85% and 75% of their incomes respectively. If their savings are in the ratio 5:6:9. Find the income of A?OptionsRs 1400Rs 1500Rs 1300Rs 1600

Question

correct answerTotal income of A, B and C is 6060 and they spend 80%, 85% and 75% of their incomes respectively. If their savings are in the ratio 5:6:9. Find the income of A?OptionsRs 1400Rs 1500Rs 1300Rs 1600

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Solution

Let's solve this step by step:

  1. The total savings of A, B, and C is the total income minus the total expenditure. Since they spend 80%, 85%, and 75% of their incomes respectively, they save 20%, 15%, and 25% of their incomes respectively.

  2. The total income of A, B, and C is Rs 6060. Let's denote the incomes of A, B, and C as a, b, and c respectively. So, a + b + c = 6060.

  3. The savings of A, B, and C are in the ratio 5:6:9. Since the savings are a certain percentage of the income, we can say that 20% of a is to 15% of b is to 25% of c as 5 is to 6 is to 9.

  4. We can write this as: 0.2a/5 = 0.15b/6 = 0.25c/9. Simplifying this, we get a/25 = b/40 = c/36.

  5. Now, we can express b and c in terms of a: b = 40a/25 = 1.6a and c = 36a/25 = 1.44a.

  6. Substituting b and c in terms of a in the equation a + b + c = 6060, we get a + 1.6a + 1.44a = 6060. Simplifying this, we get 4.04a = 6060.

  7. Solving for a, we get a = 6060 / 4.04 = Rs 1500.

So, the income of A is Rs 1500.

This problem has been solved

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