Question

A man is 56 years old and his son is 24 years old. In how many years, the father will be twice as old as his son.

Answer 1

Hint: According to the given question, firstly assume all the values which are required to solve the answer. Then substitute that with the values in the equation formed by using the given statement and hence, calculate the years at which the father will be twice as old as his son.

Complete step-by-step answer:
As it is given that the age of the father is 56 years and the age of his son is 24 years and we have to calculate the years in which the father will be twice as old as his son.
Let us consider father’s age be f and son’s age be s. And according to the question let us assume years be y.
So, \[f + y = 2(s + y)\] and here, we will calculate the value of y.
On substituting the values of f which is 56 and for s which is 24.
After substituting we get,
\[ \Rightarrow 56 + y = 2(24 + y)\]
On opening the brackets of right hand side we get,
\[ \Rightarrow 56 + y = 48 + 2y\]
Taking y on the right hand side and 48 on the left hand side.
So, we get
\[ \Rightarrow 56 - 48 = 2y - y\]
After subtracting both the values which are on the left side as well as on the right hand side.
We get the value of y that is \[y = 8\]
Hence, after 8 years the father will be twice as old as his son.

Note: To solve these types of questions, you can also verify the calculated result by putting the value of y in the equation that is \[56 + y = 2(24 + y)\]. After substituting \[y = 8\] we get \[64 = 64\] which means the right hand side is equal to the left hand side. Hence, we verified the result.