Question

The average age of A, B and C is 25 years. The Ratio of their ages is 3 : 5 : 7. Find the age of A.
(a) 21 years
(b) 18 years
(c) 15 years
(d) Data inadequate

Answer 1

Hint: First, let the age of A be 3x. Let the age of B be 5x and let the age of C be 7x. Now, find the average of their ages in terms of x and then equate it to 25. Doing this, we will get $\dfrac{3x+5x+7x}{3}=25$. Using this, find the value of x and then multiply this by 3 to get the final answer.

Complete step-by-step answer:
In this question, we are given that the average age of three boys A, B and C is 25 years. The Ratio of their ages is 3 : 5 : 7.

We need to find the age of the youngest boy A.

Since their ages are in the ratio 3 : 5 : 7.

Let the age of A be 3x. Let the age of B be 5x and let the age of C be 7x.

We are given that the average of their ages is 25 years.

So we will find the average of their ages in terms of x and then equate it to 25. Doing this, we will get the following:

$\dfrac{3x+5x+7x}{3}=25$

$15x=75$

$x=5$

Now, we assumed that the age of the youngest boy A is 3x years and we have found the value of x as 5.

So, 3x = 3 $\times $ 5 = 15 years

So, the age of A is 15 years.

Hence, option (c) is correct.

Note: In this question, it is very important to understand the ratio of ages and then suppose the boys’ ages to be 3x, 5x, and 7x, respectively. Then it is also important to find the average in terms of x and equating it to 25 to find the answer. Assuming ages like this, is the key point of solving this question.