Question

Answer the following questions considering the age of Ram is $ y $ years and he is $ \dfrac{1}{6} $ of his grandfather's age: If his grandmother's age is two years less than his grandfather's age, what is the age of his grandmother?

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Here, we need to find the present age of grandmother. We will assume the present age of Ram is $ y $ years, and he is $ \dfrac{1}{6} $ of his grandfather's age, and $ g $ for the grandfather’s age.

Complete step by step answer:
Let as the present age of Ram is $ y $ years and present age of grandfather is $ y $ $ = \dfrac{1}{6}g $ (Since grandfathers age is $ g $ and $ \dfrac{1}{6} $ of grandfather’s age)
Thus, we get the ages of Ram and the grandfather
Now the age of his grandmother is two years less that the age of the grandfather and but
Since grandfather’s age $ \Rightarrow y = \dfrac{1}{6}g $ solving this equation with cross multiplying \[6\]on left hand side we get
 $ \Rightarrow 6y = g $ which is $ \Rightarrow g = 6y $
Hence the grandfather age is $ 6y $ (Since $ y $ is the age of ram and so $ 6y $ is the age of grandfather thus if the age of ram is $ 15 $ then the age of the grandfather is 6 times the rams age which is $ 90 $ )
Therefore, by given problem the grandmothers age is two years less that the grandfathers age and
Hence $ 6y $ is the grandfathers age so then $ 6y - 2 $ will be the grandmother’s age
(Since $ 6y $ is the grandfathers age as per above example if rams age is $ 15 $ then the grandfathers age is $ 90 $ and Hence the grandmothers age will be two years lesser than the grandfather which is $ 6y - 2 = 6(15) - 2 = 90 - 2 = 88 $ )
Hence the present of the grandmother is $ 6y - 2 $

Note: Like this finding age problem we have to be careful on substituting the values of given.
Here the given age of Ram was the only present age and we used some equations to find the ages of grandfather and as well as the grandmother.