Question

# The ratio of income of two persons is $$9:7$$ and the ratio of their expenditure is $$4:3$$. If each of them saves Rs. $$200$$ per month, find their monthly income.

A
Rs. 2200, Rs. 1400
B
Rs. 2100Rs. 1400
C
Rs. 1800Rs. 1400
D
Rs. 1900Rs. 1400

Solution

## The correct option is C Rs. $$1800$$, Rs. $$1400$$The ratio of income of two persons is $$9 : 7$$ and the ratio of their expenditure is $$4 : 3$$. If each of them saves Rs. $$200$$ per month.Let income of first person be Rs. $$9x$$ and of second person be Rs. $$7x$$, then their expenditure are Rs $$4y$$ and Rs $$3y$$ respectively.For first person,                                 For second person,$$9x -4y =200$$  ....$$(1)$$                      $$7x -3y =200$$  ...$$(2)$$Multiply equation $$(1)$$ by $$3$$ and equation $$(2)$$ by $$4$$, then subtract $$(2)$$ from $$(1)$$$$27x - 12y = 600$$$$28x - 12y = 800$$  Subtracting,$$- x + 0 = -200$$ $$\Rightarrow x = 200$$put it in equation $$(1)$$$$9 \times 200 - 4y = 200$$$$y = 400$$Income of first person $$=$$ Rs. $$9 \times 200 =$$ Rs. $$1800$$and of second person is $$=$$ Rs. $$7 \times 200 =$$ Rs. $$1400$$Maths

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