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Question
The monthly incomes of A and B are in the ratio of 5:4 and their monthly expenditures are in the ratio of 7:5. If each saves Rs. 9000 per month, find the monthly income of each.
Solution
Let the monthly income of A and B are Rs.x and Rs.y respectively.
Then as per the question
`x/y = 5/4`
⇒ `y = (4x)/5`
Since each save Rs.9,000, so
Expenditure of A = Rs.(x – 9000)
Expenditure of B = Rs.(y – 9000)
The ratio of expenditures of A and B are in the ratio 7:5.
`∴(x−9000)/(y−9000) = 7/5`
⇒ 7y – 63000 = 5x – 45000
⇒ 7y – 5x = 18000
From (i), substitute y = `(4x)/5` in (ii) to get
`7 × (4x)/5 – 5x = 18000`
⇒ 28x – 25x = 90000
⇒ 3x = 90000
⇒ x = 30000
Now, putting x = 30000, we get
`y = (4 ×30000)/5 = 4 × 6000 = 24000`
Hence, the monthly incomes of A and B are Rs. 30,000 and Rs.24,000.
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