Question

Avinash’s Mother's present age is $ 6 $ times Avinash's present age. Avinash's age $ 5 $ years from now will be one third of his mother’s present age. What are their present ages?

Answer 1

Hint: Assume the present age of both Avinash and also his mother. Then form the linear equations with respect to the variables of age and then solve the equations to get their present ages.

Complete step-by-step answer:
Avinash’s Mother's present age is $ 6 $ times Avinash's present age. Avinash's age $ 5 $ years from now will be one third of his mother’s present age.
Assume that the present age of Avinash is $ x $ years and the present age of her mother is $ y $ years.
As given in the question Avinash’s Mother's present age is $ 6 $ times Avinash's present age. So, in equation form it can be written as $ y = 6x\;\;\;\;\; \ldots \left( 1 \right) $ .
It is also given that Avinash age $ 5 $ years from now will be one third of his mother’s present age. So, in equation form it can be written as $ x + 5 = \dfrac{y}{3}\;\;\;\; \ldots \left( 2 \right) $ .
Now solve both the linear equations by substituting the value of $ y $ in the second equation:
 $
\Rightarrow x + 5 = \dfrac{y}{3} \\
  x + 5 = \dfrac{{6x}}{3} \\
  x + 5 = 2x \\
  2x - x = 5 \\
  x = 5 \;
  $
The value of $ x $ is equal to $ 5 $ . So, the present age of Avinash is equal to $ 5 $ years.
Now substitute the value of $ x $ in the first equation for the value of $ y $ :
 $
\Rightarrow y = 6x \\
   = 6\left( 5 \right) \\
   = 30 \;
  $
The value of $ y $ is equal to $ 30 $ . So, the present age of Avinash’s mother is equal to $ 30 $ years.
So, the present age of Avinash and his mother is equal to $ 5 $ and $ 30 $ years respectively.
So, the correct answer is “the present age of Avinash and his mother is equal to $ 5 $ and $ 30 $ years respectively”.

Note: The conditions of the age are given as if they can be converted into linear equations of the variable of ages of avinash and his mother. Since we have to find the ages of two people, minimum two linear equations must be present.