10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

Six years hence, a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is

A) 28

B) 30

C) 32

D) 34

Correct Answer: B

Solution :

Let present age of man = x yr

and present age of son = y yr

Six years hence, men's age = (x + 6) yr,

son's age = (y + 6) yr

According to question,

\[\left( x+6 \right)=3\left( y+6 \right)\Rightarrow x+6=3y+18\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,x-3y=12\] ...(i)

and three years ago Men's age = (x - 3) yr,

son's age = (y - 3) yr

According to the question,

\[\left( x-3 \right)=9\left( y-3 \right)\]

\[\Rightarrow \,\,\,\,x-3=9y-27\]

\[\Rightarrow \,\,\,\,\,\,\,x-9y=-24\] ...(ii)

On subtracting Eq. (ii) from Eq. (i), we get

\[6y=36\Rightarrow \,\,y=6\]

On substituting the value of y in Eq. (i),

we get

\[x-18=12\Rightarrow x=30\,yr\]