Question

The ratio of Sam's and Rahul's income is 5:4 and the ratio of their expenditures is 3:2. If at the end of the year each saves ₹1600, then Sam's income is

• A. ₹1600
• B. ₹3200
• C. ₹4000
• D. ₹2400

Answer 1

The correct option is C ₹4000

Let the income of Sam and Rahul be $5x$ and $4x$, and their expenditures be $3y$ and $2y$ respectively.
$⟹$Sam's savings = $5x-3y$ and Rahul's savings= $4x-2y$
By question, $5x-3y=1600...\left(1\right)$
$4x-2y=1600...\left(2\right)$.
Multiplying (1) by 2 and (2) by 3, we have $10x-6y=3200...\left(3\right)$
$12x-6y=4800...\left(4\right)$.
Subtracting (3) from (4), $2x=1600⟹x=800$
Thus, Sam's income=$5x=5\times 800=₹4000$