Question

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

• A. $Rs.3400$
• B. $Rs.3600$
• C. $Rs.4000$
• D. $Rs.4400$

Answer 1

Answer: (C)

$Rs.4000$

Let the income of A be 5k and that of B be 4k.

Let expenditure of A be 3x and that of B be 2x.

So

$5k-3x=1600$ (1)

$4k-2x=1600$ (2)

Dividing (2) by 2

$2k-x=800$

$2k-800=x$ (3)

Substituting (3) in (1)

$5k-3(2k-800)=1600$

$5k-6k+2400=1600$

$-k=-800$

$k=800$

Income of A$=5k=5\left(800\right)=4000Rs$