The monthly income of A, B and C taken together is Rs. 69,000. A spends 70% of income, B spends 80% of income and C spends 92% of income. If their monthly savings are in the ratio of 15 : 11 : 10, respectively, then the monthly savings (in Rs.) of B is:
Question
The monthly income of A, B and C taken together is Rs. 69,000. A spends 70% of income, B spends 80% of income and C spends 92% of income. If their monthly savings are in the ratio of 15 : 11 : 10, respectively, then the monthly savings (in Rs.) of B is:
Solution
To solve this problem, we need to follow these steps:
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First, we need to understand that the savings of a person is the income that is not spent. So, if A spends 70% of his income, he saves 30%. Similarly, B saves 20% and C saves 8% of their respective incomes.
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The problem states that the savings of A, B, and C are in the ratio of 15:11:10. This means that if we add up the parts of this ratio, we get a total of 36 parts.
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Each part of this ratio represents a certain amount of the total savings of A, B, and C. To find the value of one part, we divide the total savings (which is the total income minus the total expenses) by the total number of parts. The total income of A, B, and C is Rs. 69,000. The total expenses are 70% of A's income, 80% of B's income, and 92% of C's income. Since we don't know the individual incomes yet, we can't calculate the total expenses. However, we know that the total savings (income - expenses) are divided into 36 parts.
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We can express the savings of A, B, and C as percentages of their respective incomes: A saves 30% of his income, B saves 20% of his income, and C saves 8% of his income. These savings are in the ratio of 15:11:10. So, we can write the following equations:
30% of A's income = 15 parts 20% of B's income = 11 parts 8% of C's income = 10 parts
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From these equations, we can express A's, B's, and C's incomes in terms of 'parts':
A's income = 15 parts / 30% = 50 parts B's income = 11 parts / 20% = 55 parts C's income = 10 parts / 8% = 125 parts
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The total income of A, B, and C is the sum of these parts, which is 50 parts + 55 parts + 125 parts = 230 parts. Each part, therefore, is worth Rs. 69,000 / 230 = Rs. 300.
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The monthly savings of B is 11 parts, so it is 11 parts * Rs. 300/part = Rs. 3300.
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