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

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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