Question

The sum of Raju’s age and half of Sameer’s age is 4. One third Raju’s age added to twice Sameer’s age is 5. Find twice the difference of their ages.

Answer 1

Is the answer 2??????

Answer 2

Let the age of Raju be x and age of Sameer be y

From first condition,

$x + \frac{y}{2} = 4$

$2x + y = 8...............(1)$

FROM SECOND CONDITION,

$\frac{x}{3} + 2y = 5$

$x + 6y = 15............(2)$

Multiply (2) by 2

$2(x + 6y) = 2(15)$

$2x + 12y = 30............(3)$


Subtract (1) from (3)


$(2x + 12y) - (2x + y) = (30) - (8)$
$2x + 12y - 2x - y = 22$
$2x - 2x + 12y - y = 22$


$11y = 22 \\ \\ y = \frac{22}{11} \\ \\ y = 2$

From (1)

$2x + y = 8 \\ \\ 2x + (2) = 8 \\ \\ 2x = 8 - 2 \\ \\ 2x = 6\\ \\ x = \frac{6}{2} \\ \\ x = 3$
Thus, Raju's age is 3 years and Sameer's age is 2 years