Question

A girl is 28 years younger than her father . The sum of their ages is 50 . Find the ages of the girl and the father.

Answer 1

Hint:
At first we need to take the age of the girl to be x and with the given condition that the girl is 28 years younger than her father we get the age of the father to be $x + 28$ years and using the condition that the sum of their ages is 50 we get the value of x which gives the age o the girl and using which we can find the age of the father.

Complete step by step solution:
Now let us assume the age of the girl to be x years
We are given that the girl is 28 years younger than her father
This clearly says that her father is 28 years older than his daughter
Hence his age is $x + 28$ years
We are given that the sum of their ages is 50
Hence
$
   \Rightarrow x + x + 28 = 50 \\
   \Rightarrow 2x + 28 = 50 \\
   \Rightarrow 2x = 50 - 28 \\
   \Rightarrow 2x = 22 \\
   \Rightarrow x = \dfrac{{22}}{2} = 11 \\
 $
Hence from this we get the age of the girl to be 11 years
We can get the age of the father by using the value of x in the fathers age
$ \Rightarrow x + 28 = 11 + 28 = 39$

Therefore the age of the father is 39 years.

Note:
The same problem can be done by taking the fathers age to be x
Let the fathers age be x
And the daughter is 28 years younger hence the age of the daughter is $x - 28$
Since the sum of their age is 50
$
   \Rightarrow x + x - 28 = 50 \\
   \Rightarrow 2x - 28 = 50 \\
   \Rightarrow 2x = 50 + 28 \\
   \Rightarrow 2x = 78 \\
   \Rightarrow x = \dfrac{{78}}{2} = 39 \\
 $
Hence from this we get the age of the father to be 39 years
We can get the age of the daughter by using the value of x in the fathers age
$ \Rightarrow x - 28 = 39 - 28 = 11$
Therefore the age of the daughter is 11 years