A man is 3 years older than his wife and four times as old as his son. If the son becomes 15 years old after 3 years. Then what is the present age of the wife?
1). 60 years
2). 51 years
3). 48 years
4). 45 years
Solution;
Let the man's age be 'x' his wife's age be 'y' and his son's age be 'z'.
It is given that the man is 3 years older than his wife and four times as old as his son so,
$x = y + 3 -------> 1$
$x = 4z -----------> 2 $
It is also given that the man's son become 15 years old after 3 years so,
$z + 3 = 15$
So, $z = 15 - 3 = 12$
Substituting the value of z in equation 2 we get
$x = 4 × 12$
$x = 48$
Substituting the value of x in equation 1 we get
$48 = y + 3$
$y = 48 - 3$
$y = 45$
So, the present age of the man's wife is 45 years.
The correct option is 4). 45 years