Question

Raman’s age is three times the sum of the ages of his two sons. After 5 years his age will be twice the sum of the ages of his two sons. Find the age of Raman.

Answer 1

Answer:

Raman is 45 years old.

Step-by-step explanation:

Let the age of Raman be 'x', and the sum of ages of his two sons be 'y'.

It is given that Raman's age is 3 times the sum of the ages of his two sons.

Therefore, x=3y      (1)

It is also given that after 5 years, Raman's age will be twice the sum of the ages of his two sons.

Therefore, x+5 = 2(y+5+5)

x+5 = 2y + 20       (2)

Substitute with x=3y in equation (2):

3y+5 = 2y +20

y = 15

Therefore, x = 3(15) = 45 years old.

Answer 2

Let the sum of ages of his sons are = x years

and the age of Raman is = y years

So, according to the question

Raman’s age is three times the sum of the ages of his two sons:
$y = 3x \: \: \: eq1$
After 5 years,all are five year older,so

$(y + 5) = 2(x + 10) \\ \\ y - 2x = 15 \: \: \: eq2$
put the value of y from eq1 in eq2

$3x - 2x = 15 \\ \\ x = 15$
So, age of Raman is = 3×15= 45 years