# What is ‘A’ income?

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, A’s income is:

- Rs. 4000
- Rs. 5500
- Rs. 6000
- Rs. 3500

**Answer: (3) Rs. 6000**

**Explanation:-
**The ratio of the incomes of A and B = 3: 2

Let the income of A = 3X and the income of B = 2X

The ratio of their expenditure = 5: 3

Then, let the expenditure of A = 5 Y and the expenditure of B = 3Y

If each saves Rs. 1000,

Then, 3 X – 5 Y = 1000 ……………… (1)

2 X – 3 Y = 1000 ……………. (2)

In equation (1) multiply by 2 & in equation (2) multiply by 3,

Then, 6 X – 10 Y = 2000 ………………… (3)

6 X – 9 Y = 3000 ……………………… (4)

Subtract equation (4) from equation (3),

Then, 6 X – 10 Y – 6 X + 9 Y = 2000 – 3000

– Y = -1000

Y = 1000

Put the value of Y in equation (1),

Then, 3 X – 5 x 1000 = 1000

3 X – 5000 = 1000

3 X = 1000 + 5000

3 X = 6000

X = 6000/3

X = 2000

Then, the income of A = 3 X = 3 x 2000

= Rs. 6000

Hence, the answer is (3) Rs. 6000.