The incomes of A and B are in the ratio 3:2 and their expenditure are in the ratio 5:3.If each saves Rs 1000 then what is the A's income?

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Solution

$Let the income of A and B are Rs 3 x and Rs 2 x . Let the expenditure of A and B are Rs 5 y and Rs 3 y Now, according to question, 3 x - 5 y = 1000 . . . . . . (1) 2 x - 3 y = 1000 . . . . . . . (2) Multiply (1) by 2 and (2) by 3, we get 6 x - 10 y = 2000 . . . . . . . (3) 6 x - 9 y = 3000 . . . . . . . (4) Subtracting (3) from (4), we get (6 x - 9 y) - (6 x - 10 y) = 3000 - 2000 \Rightarrow y = 1000 Put y = 1000 in (1), we get 3 x - 5 (1000) = 1000 \Rightarrow 3 x - 5000 = 1000 \Rightarrow 3 x = 6000 \Rightarrow x = \frac{6000}{3} = 2000 So, the income of A = Rs 3 x = 3 \times (2000) = Rs 6000$

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