Question

The mean age of three students Vijay, Rahul and Anu is 15 years. If there are in the ratio 4: 5: 6 respectively, their ages are
$
  (a){\text{ 12 years, 15 years, 18 years}} \\
  (b){\text{ 12 years, 18 years, 15 years}} \\
  (c){\text{ 18 years, 15 years, 12 years}} \\
  (d){\text{ 15 years, 12 years, 18 years}} \\
$

Answer 1

Hint: In this question the mean as well as the ratio of ages of the three students is given in the question. 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 ration of ages to calculate the variable ages for each candidate.

Complete step-by-step answer:

It is given that the mean age of three students Vijay, Rahul and Anu is 15 years.

Let the age of Vijay be x years.

Age of Rahul be y years.

And the age of Anu be z years.

So the mean age of these three students is
$ \Rightarrow \dfrac{{x + y + z}}{3} = 15$
$ \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 4 : 5 : 6 respectively.

Therefore age of Vijay $ = \dfrac{4}{{4 + 5 + 6}}\left( {{\text{sum of their ages}}} \right)$
$ \Rightarrow x = \dfrac{4}{{15}}\left( {45} \right) = 4\left( 3 \right) = 12$ Years.

Similarly,
$ \Rightarrow y = \dfrac{5}{{15}}\left( {45} \right) = 5\left( 3 \right) = 15$ Years.
$ \Rightarrow z = \dfrac{6}{{15}}\left( {45} \right) = 6\left( 3 \right) = 18$ Years.

Therefore the age of Vijay, Rahul and Anu is 12, 15 and 18 years respectively.
Hence option (A) is correct.

Note: Whenever we face such types of problems the key concept is to have the 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.