The ratio of income of A to that of B is 5 : 4 and the expenditure of A to that of B is 3: 2. If at the end of the year, each saves Rs, 800, the income of A is:
Question
The ratio of income of A to that of B is 5 : 4 and the expenditure of A to that of B is 3: 2. If at the end of the year, each saves Rs, 800, the income of A is:
Solution
Let's solve this step by step:
Step 1: Let's assume the income of A and B as 5x and 4x respectively. Similarly, let's assume the expenditure of A and B as 3y and 2y respectively.
Step 2: According to the problem, both A and B save Rs. 800 at the end of the year. So, we can write the equations as:
Income - Expenditure = Savings
For A: 5x - 3y = 800 ---- (Equation 1)
For B: 4x - 2y = 800 ---- (Equation 2)
Step 3: Now, we can solve these two equations to find the values of x and y. Let's multiply Equation 2 by 3 and Equation 1 by 2 and then subtract Equation 1 from Equation 2.
12x - 6y = 2400 10x - 6y = 1600
2x = 800
So, x = 800 / 2 = 400
Step 4: Substitute x = 400 in Equation 1:
5*400 - 3y = 800 2000 - 3y = 800 3y = 2000 - 800 3y = 1200 y = 1200 / 3 = 400
Step 5: Now that we have the values of x and y, we can find the income of A which is 5x. So, the income of A = 5*400 = Rs. 2000.
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