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Answer :
The savings of A, B, and C (given their income and spending ratios and that A saves 1/4th of his income) are in the ratio 57:40:9, which is found through a step-by-step calculation of each individual's savings by using the given ratios. Therefore correct option is A
The question asks to find the ratio of the savings of individuals A, B, and C, given that their incomes are in the ratio of 7:9:12, their spendings are in the ratio of 8:9:15, and A saves 1/4th of his income. To solve this, we must first express the savings of each individual in terms of their income (minus spending).
Let the incomes of A, B, and C be 7x, 9x, and 12x respectively, and the spendings be 8y, 9y, and 15y, respectively. Since A saves 1/4th of his income, we have:
- Savings of A = 7x - 8y
- Savings of B = 9x - 9y
- Savings of C = 12x - 15y
However, we know that A saves 1/4th of his income, so Savings of A = 7x - (1/4 * 7x) = (3/4) * 7x = 5.25x.
We can now equate A's spending in terms of y using the spending ratio: 8y = (7x/4), which gives us y = (7x/32). Plugging the y value into the savings of B and C, we get:
- Savings of B = 9x - (9 * 7x/32)
- Savings of C = 12x - (15 * 7x/32)
After calculating, we get the following savings for B and C:
- Savings of B = 9x - (63x/32)
- Savings of C = 12x - (105x/32)
Rationalizing the savings amounts and finding a common numerator for A, B, and C will give us the ratio of the savings.
After simplifying we find that the ratio of the savings for A, B, and C to be 57:40:9, which corresponds to option A on the question paper.
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