The ratio of the incomes of A and B is 5:4 an | vedclass

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(C) Let the incomes of $A$ and $B$ be $5x$ and $4x$ respectively.Let the expenditures of $A$ and $B$ be $3y$ and $2y$ respectively.We know that $	ext

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$4000$

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(C) Let the incomes of $A$ and $B$ be $5x$ and $4x$ respectively.Let the expenditures of $A$ and $B$ be $3y$ and $2y$ respectively.We know that $	ext{Income} - 	ext{Expenditure} = 	ext{Saving}$.For $A$: $5x - 3y = 1600$  ---$(1)$For $B$: $4x - 2y = 1600$  ---$(2)$To solve these equations,multiply equation $(1)$ by $2$ and equation $(2)$ by $3$:$10x - 6y = 3200$  ---$(3)$$12x - 6y = 4800$  ---$(4)$Subtracting equation $(3)$ from $(4)$:$(12x - 10x) = 4800 - 3200$$2x = 1600$$x = 800$Therefore,the income of $A = 5x = 5 	imes 800 = 4000$ $Rs.$

The ratio of the incomes of $A$ and $B$ is $5:4$ and the ratio of their expenditures is $3:2$. If at the end of the year,each saves $Rs. 1600$,then the income of $A$ is (in $Rs.$):

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