Question

Sonu’s grandmother is 80 years old and Sonu is 20 years old . How many years ago was his grandmother 7 times as old as Sonu?

Answer 1

Hint: We are given the age of the grandmother and Sonu . And let's assume the number of years before which the age of the grandmother will be seven times his age be X years . By this we obtain the equation $(80 - X) = 7(20 - X)$.Solving this gives us the required number of years .

Complete step-by-step answer:
We are given that the age of Sonu’s grandmother is 80 years and and Sonu’s age is 20 years
And X years ago the age of his grandmother is seven times as Sonu
That is ,
$ \Rightarrow (80 - X) = 7(20 - X)$
We can get the value of X by solving the equation above and it will gives the number of years before which the age of his grandmother was seven times his age
$
   \Rightarrow 80 - X = 140 - 7X \\
   \Rightarrow 7X - X = 140 - 80 \\
   \Rightarrow 6X = 60 \\
   \Rightarrow X = \dfrac{{60}}{6} = 10 \\
$
Therefore 10 years before the age of the grandmother is 70 and the age of sonu is 10
We can see that the age of the grandmother is seven times his age
Therefore the answer is 10 years.

Note: Points to remember
1.If the present age is y, then n times the present age = ny.
2.If the present age is x, then age n years later/hence = x + n.
3.If the present age is x, then age n years ago = x – n.
4.The ages in a ratio a: b will be ax and bx.