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

5 years hence, the age of a man shall be 4 times the age of his son while 3 years earlier the age of the man was 16 times the age of his son. The present age of the man is:

A) 35 years

B) 40 years

C) 37 years

D) 30 years

Correct Answer: A

Solution :

[a] Let the present age of man be x years and that of his son be y years.

According to the question.

\[x+5=4(y+5)\,\,\,\Rightarrow \,\,\,x-4y-15=0\] ...(1)

and\[x-3=16(y-3)\,\,\Rightarrow \,\,x-16y+45=0\] ....(2)

Subtracting eq. (2) from eq. (1), we get

\[12y-60=0\,\,\Rightarrow \,\,y=5\]

Substituting the value of y in eq. (1), we get

\[x-4(5)-15=0\,\,\Rightarrow \,\,\,x=35\]

Hence, the present age of man is 35 years.