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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 manages to save Rs. $$2000$$ per month, find their monthly income. 


A
Rs.18,000,Rs.14,000 
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B
Rs.1,000,Rs.14,000 
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C
Rs.18,000,Rs.1,000 
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D
None of these
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Solution

The correct option is C $$Rs. 18,000 , Rs. 14,000$$ 
Let their salaries be $$9x$$ and $$7x$$.
Let their expenditure be $$4y$$ and $$3y$$.

According to the question,
$$9x-4y=2000$$           $$—(1)$$
$$7x-3y=2000$$            $$—(2)$$

From $$(1)$$
$$x=\dfrac{2000+4y}{9}$$              $$—(3)$$

On putting $$x$$ in $$(2)$$, we get
$$7\times \dfrac{(2000+4y)}{9}-3y=2000$$

$$\dfrac{(14000+28y)}{9}-3y=2000$$

$$\dfrac{14000+28y-27y}{9}=2000$$

$$14000+y=18000$$

$$y=4000$$

Now, put $$y$$ in (3)
$$x=\dfrac{2000+4\times 4000}{9}$$

$$x=\dfrac{2000+16000}{9}$$

$$x=\dfrac{18000}{9}=2000$$

So,
Salary of first person $$=9\times 2000=Rs.\ 18000$$
Salary of second person $$=7\times 2000=Rs.\ 14000$$

Hence, this is the answer.

Mathematics

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