Question

After 32 years, Rahim will be 5 times as old as he was 8 years ago. How old is Rahim today?

Answer 1

Hint:
In the given question, we have been asked to find the present age of Rahim and it is given that after 32 years, Rahim will be 5 times as old as he was 8 years ago. First we need to let the present age then we will fill the age of Rahim 8 years ago and age of the Rahim after 32 years. Then considering the given statement in the question, we will form an equation and equate the above formed equation with each other and solve for the variable. In this way we will get the present age of Rahim.

Complete step by step solution:
We have given that,
After 32 years, Rahim will be 5 times as old as he was 8 years ago.
Let the present age of Rahim be ‘x’ years.
8 years ago;
Rahim’s age 8 years ago would be = (x – 8) years
Now,
After 32 years from the present age;
Rahim’s age after 32 years will be = (x + 32) years------- (1)
According to the question,
After 32 years, Rahim will be 5 times as old as he was 8 years ago.
Converting into numerical form;
After 32 years,
Rahim’s age will be = \[5\left( x-8 \right)\]------ (2)
On equating equation (1) and equation (2), we obtained
\[\Rightarrow x+32=5\left( x-8 \right)\]
Now, solving for the value of ‘x’.
Simplifying the above equation, we get
\[\Rightarrow x+32=5x-40\]
Subtracting 32 from both the sides of the equation, we get
\[\Rightarrow x=5x-72\]
Subtracting 5x from both the sides of the equation, we get
\[\Rightarrow -4x=-72\]
Dividing both the sides of the equation by -4, we get
\[\Rightarrow x=18\]
Therefore,
The present age of Rahim is ‘x’ which is equal to 18 years.
Rahim’s today age is 18 years.
Hence, it is the required answer.

Note:
While solving these types of age related question, we will need to remember some important points;
1) If the present age is ‘y’, then ‘n’ times the present age will be equal to ‘ny’.
2) If the present age is ‘y’, then 8 years ago the age will be y – 8.
3) If the present age is ‘y’, then after 10 years the age will be y + 10.
4) The ratio the ages i.e. x : y will be equal to ax and ay.