The income of A, B and C are in the ratio 7: 9: 12 and their expenditure are in the ratio 8 : 9 : 15. If a saves 1/4 of his income. Find the ratio of savings of A, B and C.
Question
The income of A, B and C are in the ratio 7: 9: 12 and their expenditure are in the ratio 8 : 9 : 15. If a saves 1/4 of his income. Find the ratio of savings of A, B and C.
Solution
Sure, let's solve this step by step.
Step 1: Let's assume the incomes of A, B, and C as 7x, 9x, and 12x respectively. Similarly, let's assume their expenditures as 8y, 9y, and 15y respectively.
Step 2: According to the problem, A saves 1/4 of his income. So, A's savings will be 1/4 * 7x = 7x/4.
Step 3: Now, we know that savings is income minus expenditure. So, we can find the expenditures of A, B, and C by rearranging the savings equation: expenditure = income - savings.
For A: 8y = 7x - 7x/4. Solving this we get y = x/2.
Step 4: Now, substitute y = x/2 in the expenditure of B and C to find their savings.
For B: Savings = income - expenditure = 9x - 9y = 9x - 9*(x/2) = 9x/2.
For C: Savings = income - expenditure = 12x - 15y = 12x - 15*(x/2) = 3x/2.
Step 5: Now, we have the savings of A, B, and C as 7x/4, 9x/2, and 3x/2 respectively.
So, the ratio of their savings is (7x/4) : (9x/2) : (3x/2) = 7 : 18 : 6.
Therefore, the ratio of savings of A, B, and C is 7 : 18 : 6.
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