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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
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B
Rs. 2100Rs. 1400
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C
Rs. 1800Rs. 1400
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D
Rs. 1900Rs. 1400
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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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