Question

The fathers age one year back is 4 times the age of son, after 6 years the father's age exceeds twice the age of the son by 9. What is fathers age?
33
42
56
28​

Answer 1

Question:-

• The fathers age one year back is 4 times the age of son, after 6 years the father's age exceeds twice the age of the son by 9. What is fathers age?

To Find:-

• Find the fathers age.

Given:-

• The fathers age one year back is 4 times the age of son, after 6 years the father's age exceeds twice the age of the son by 9.

Solution:-

Let the present of father be x years

Present age of son be y years

According to Question:-

$\tt\implies \: x - 1 = 4( y - 1 ) [/ex]</p><p></p><p>[tex]\tt\implies \: x - 4y = - 3 . . . . ( i )$

Now ,

$\tt\implies \: x + 6 = 2( y + 6 ) + 9$

$\tt\implies \: x - 2y = 15 . . . . ( ii )$

Now ,

We have to Subtract ( ii ) from ( i )

$\tt\implies \: x - 4y - ( x - 2y ) = - 3 - 15$

$\tt\implies \: x - 4y - x + 2y = - 18$

$\tt\implies \: - 2y = - 18$

$\tt\implies \: x = \cancel\dfrac { - 18 } { - 2 }$

Substitute in equation ( i ) to get x value:-

$\tt\implies \: x - 4y = - 3 . . . . ( i )$

$\tt\implies \: x = 33$