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The incomes of A and B are in the ratio 7 : 9. and their expenditures are in the ratio 3:5. Ifeach one saves 1200 Rs, then what is the income of A?

Question

The incomes of A and B are in the ratio 7 : 9. and their expenditures are in the ratio 3:5. Ifeach one saves 1200 Rs, then what is the income of A?

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Solution

Let's solve this step by step:

Step 1: Let's assume the incomes of A and B as 7x and 9x respectively. Similarly, let's assume their expenditures as 3y and 5y.

Step 2: According to the problem, both A and B save Rs. 1200. So, we can write the equations as:

Income - Expenditure = Savings

For A: 7x - 3y = 1200 ----(Equation 1)

For B: 9x - 5y = 1200 ----(Equation 2)

Step 3: Now, we can solve these two equations to find the values of x and y. Let's multiply Equation 1 by 5 and Equation 2 by 3 and then subtract Equation 2 from Equation 1.

35x - 15y = 6000 and 27x - 15y = 3600

Subtracting these gives: 8x = 2400

So, x = 2400 / 8 = 300

Step 4: Substitute x = 300 in Equation 1, we get:

7*300 - 3y = 1200

2100 - 3y = 1200

3y = 2100 - 1200 = 900

So, y = 900 / 3 = 300

Step 5: Now that we have the values of x and y, we can find the income of A which is 7x.

So, Income of A = 7*300 = Rs. 2100.

This problem has been solved

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