Question

Father is aged three times more than his son Ronit. After 8 years, he would be two and half times Ronit's age. After further 8 years, how many times would he be of Ronit’s age?
A.\[2\] times
B.\[2\dfrac{1}{2}\] times
C. \[2\dfrac{3}{2}\] times
D.\[3\] times

Answer 1

Hint: In solving these types of question we consider the age of the given person will be \[x\].Using the given condition in given word problem we can make use of it and convert it into equation and then we solve for \[x\].These equations could become either linear or nonlinear. These equations will have solutions that will represent the age of the people in the question.

Complete step-by-step answer:
Let Ronit present age be \[x\].
Given, the father is aged three times more than his son Ronit. Then present age of Father will be \[3x\]
After 8 years, he would be two and half times Ronit's age.
Thus after 8 years, the age of Ronit is \[x + 8\] and Ronit’s father is \[3x + 8\].
Then, \[ \Rightarrow 3x + 8 = 2.5(x + 8)\]
\[ \Rightarrow 3x + 8 = 2.5x + 20\]
\[ \Rightarrow 3x - 2.5x = 20 - 8\]
\[ \Rightarrow 0.5x = 12\]
\[ \Rightarrow x = \dfrac{{12}}{{0.5}}\]
\[ \Rightarrow x = \dfrac{{120}}{5}\]
Thus \[x = 24\] Years.
Thus Ronit age is \[24\] and his father age is given by
\[ \Rightarrow 3x = 3 \times 24 = 72\] Years.
After \[8\] years Ronit age will be \[24 + 8 = 32\] Years.
His father’s age is \[72 + 8 = 80\] Years.
Now the ratio of father age to Ronit age \[ = \dfrac{{80}}{{32}} = 2.5\] Years.
So, the correct answer is “Option B”.

Note: In this type of question read the problem carefully. We convert the word problem into an equation. Because equations are a convenient way to represent conditions or relations between two or more quantities. Since only one variable is present in the equation we can solve it easily. Be carefully about present age and after age. If we find after age we use addition.