# Find the Difference in Their Monthly Incomes :

A and B have their monthly incomes in the ratio 8:5, while their monthly expenditures are in the ratio 5:3, If they have saved ₹ 12,000 and ₹ 10,000 monthly respectively, then the difference in their monthly incomes is

- ₹ 52,000
- ₹ 44,000
- ₹ 46,000
- ₹ 42,000

**Answer is (4): Rs. 42,000**

**Explanation:-**The ratio of the income of A and B = 8: 5

Let the income of A be = 8 X and the income of B = 5 X

The ratio of their expenditures = 5: 3

Let the expenditure of A = 5 Y & the expenditure of B = 3 Y

Then, 8 X – 5 Y = 12, 000 ………………………………. (1)

5 X – 3 Y = 10, 000 ……………………………………….(2)

In equation (1) multiply by 3 & in equation (2) multiply by 5

Then, 24 X – 15 Y = 36, 000 ………………(3)

25 X – 15 Y = 50, 000 …………(4)

equation (3) is subtracted from (4),

Then, 25 X – 24 X – 15 Y + 15 Y = 50, 000 – 36, 000

X = 14, 000

Then, the monthly in come of A =8 X = 8 x 14, 000

= 1, 12, 000

And the monthly income of B = 5 X = 5 x 14, 000

= 70, 000

Then, the difference between their monthly income = 1, 12, 000 – 70, 000

= Rs. 42, 000

Hence, the answer is (4) Rs. 42, 000