Chapter 6.4, Problem 20P

In 4 years, a mother will be 5 times as old as her daughter. At present, the mother is 9 times as old as the daughter. How old are the mother and the daughter today?

To determine

To find: The present age of mother and daughter.

Answer to Problem 20P

The present age of mother is 36 years and daughter is 4 years.

Explanation of Solution

Given information: In 4 years, a mother will be 5 times as old as her daughter. At present, the mother is 9 times as old as the daughter.

Calculation: Let the present age of daughter be x years.

Then, present age of mother is 9x years.

After 4 years, age of daughter will be $x+4$ years and age of mother will be $9x+4$ years.

According to the problem,

  $\begin{array}{l}9x+4=5(x+4)\\ \Rightarrow 9x+4=5x+20\\ \Rightarrow 9x-5x=20-4\\ \Rightarrow 4x=16\\ \Rightarrow x=4\end{array}$

  $\therefore$ The present age of daughter $=4$ years

  $\therefore$ The present age of mother $=9x=9\cdot 4=36$ years

Thus, present age of mother is 36 years and daughter is 4 years.