Question

The average age of three people is 60 years. The age of the first person is 1/4 of the total age of the other two persons. What is the age of the first person?
A) 46 B) 56 C) 36 D) 66

Answer 1

Hint: In order to solve this type of problems related to age, we need to follow the following steps:-
a.) Express what we don't know as a variable.
b.) Create an equation based on the information provided.
c.) Solve for the unknown variable.
d.) Substitute our answer back into the equation to see if the left side of the equation equals the right side of the equation and hence, we will get our final result.

Complete step-by-step answer:
We are provided here with the ages of three people.
So, let the age of first person be x,
         let the age of second person be y,
         let the age of third person be z,
According to the question;
Average age of three person is 60 years;
$ \Rightarrow x + y + z = 60 \times 3$
$ \Rightarrow x + y + z = 180$ …………………(i)
Now, It's given that;
 Age of the first person is 1/4 of the total age of the other two.
$ \Rightarrow x = \dfrac{1}{4}\left( {y + z} \right)$
$ \Rightarrow 4x = y + z$ ……………….(ii)
Substituting equation (2) in equation (1);

$ \Rightarrow x + y + z = 180$
$ \Rightarrow x + 4x = 180$
$ \Rightarrow 5x = 180$
$ \Rightarrow x = \dfrac{{180}}{5}$
$ \Rightarrow x = 36$years
$\therefore $Age of the first person is 'x' years that is 36 years.
Therefore, option (c) is the correct answer for this particular question.

Note: In order to solve age related problems, we need no some of the important points which are as follows:-
a.) If the present age is y, then n times the present age = ny.
b.) If the present age is x, then age n years later/hence = x + n.
c.) If the present age is x, then age n years ago = x – n.
d.) The ages in a ratio a: b will be ax and bx.