the incomes of A and B are in the ratio 3:2 and their expenditures are in the of 5:3.if each saves Rs.1000 then find A's income

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Solution

Let the income of A and B be 3x and 2x; and the expenditures be 5y and 3y respectively.

Then, according to the question,

3x – 5y = 1000 .....(1)

2x – 3y = 1000 ......(2)

On multiplying equation (1) by 2 and equation (2) by 3:

6x – 10y = 2000 (3)

6x – 9y = 3000 (4)

Subtracting equation (3) from equation (4)

6x – 9y – 6x + 10y = 3000 – 2000

y = 1000

On putting y = 1000 into (1),

3x – 5 × 1000 = 1000

3x = 1000 + 5000

3x = 6000

x = 2000

Thus, A's income = 3x = Rs 3 × 2000 = Rs 6000

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