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

The father's age is six times his son's age. Four years hence, the age of the father. will be four times his son's age. The present ages, in years of the son and the father are, respectively: (NCERT EXEMPLAR)

A) 4 and 24

B) 5 and 30

C) 6 and 36

D) 3 and 24

Correct Answer: C

Solution :

[c] Let the present age of father is x years and the present age of son is y years.

According to the question, \[(x+4)=4(y+4)\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,x-4y=12\] ...(1)

and \[x=6y\] ...(2)

Substituting the value of x from eq. (2) in eq. (1), we get

\[2y=12\,\,\Rightarrow y=6\]

When \[y=6,\] then from eq. (2), \[x=36\]

Hence, present age of father is 36 years and present age of son is 6 years.