# 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:

1. Rs. 4000
2. Rs. 5500
3. Rs. 6000
4. Rs. 3500
Monis Rasool Professor Asked on 25th October 2015 in

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.

Anurag Mishra Professor Answered on 26th October 2015.