Question

The average age of three boys is 15 years. If their ages are in the ratio 3:5:7, the age of the youngest boy is
A. 21 years
B. 18 years
C. 15 years
D. 9 years

Answer 1

Hint: In this question the mean, as well as the ratio of ages of the three boys, are given. Mean refers to the sum of ages divided by the total number of students, in this case, use this concept along with the relation given in terms of the ratio of ages to calculate the variable ages for the youngest boy.

Complete step-by-step solution:
It is given that the mean age of three boys is 15 years.
Let the age of the youngest boy be x years, the age of the middle one be y years and the eldest be z years.
So, the mean age of these three boys is,
$ \Rightarrow \dfrac{{x + y + z}}{3} = 15$
Multiply both sides by 3 and simplify it,
$ \Rightarrow x + y + z = 45$
Therefore, the sum of their ages is 45.
Now it is also given that their ages are in the ratio 3 : 5: 7 respectively.
So, the age of the youngest boy will be given by,
$ \Rightarrow x = \dfrac{3}{{3 + 5 + 7}} \times \left( {x + y + z} \right)$
Substitute the values,
$ \Rightarrow x = \dfrac{3}{{3 + 5 + 7}} \times 45$
Simplify the terms,
$ \Rightarrow x = \dfrac{{135}}{{15}}$
Divide numerator by denominator on the right side,
$\therefore x = 9$
Therefore, the age of the youngest boy is 9 years respectively.

Hence, option (D) is the correct answer.

Note: Whenever we face such types of problems the key concept is to have a basic understanding of the mean. Always start by considering the unknown ages as variables and then use the information provided in the question to form the equations involving these variables. Evaluation of these variables will help in getting the answer.
A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.