A and B do a business together. Their incomes are in the ratio 3 : 2, and their expenses are in the ratio 5 : 3. If each saves Rs. 1000, what are their incomes?

Explanation

Let A and B’s incomes be 3x and 2x, respectively.  

Let their expenses be 5y and 3y, respectively.  

Their savings = Income − Expense = Rs. 1000 for both.

So:

For A:  

3x − 5y = 1000  → (1)

For B:  

2x − 3y = 1000  → (2)

Multiply (1) by 2:  

6x − 10y = 2000

Multiply (2) by 3:  

6x − 9y = 3000

Now subtract:  

(6x − 10y) − (6x − 9y) = 2000 − 3000  

⇒ −y = −1000  

⇒ y = 1000

Now plug y = 1000 into equation (1):  

3x − 5(1000) = 1000  

⇒ 3x = 6000  

⇒ x = 2000

Now find incomes:  

A's income = 3x = 6000  

B's income = 2x = 4000 

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