Three boys, on an average, are 25 years old, and their age are in the ratio of 3 : 5 : 7. What is the age of youngest boy?

The correct answer is 15 years.

Step 1: Understand the given information

We are given that:

1. The average age of three boys is 25 years.
2. The ages of the three boys are in the ratio $3:5:7$.

Step 2: Find the total sum of their ages

The formula for the average is:

$\text{Average}=\frac{\text{Sum of ages}}{\text{Total number of boys}}$

Using the given average of 25 years for 3 boys, we can calculate the total sum of their ages:

$\text{Sum of ages}=25\times 3=75\text{years}$

Step 3: Represent their ages using a common variable

Since their ages are in the ratio $3:5:7$, let the ages of the three boys be $3x$, $5x$, and $7x$, where $x$ is a constant multiplier.

Step 4: Set up the equation and solve for $x$

The sum of their ages is equal to 75 years:

$3x+5x+7x=75$

$15x=75$

$x=\frac{75}{15}$

$x=5$

Step 5: Calculate the age of the youngest boy

The youngest boy corresponds to the smallest part of the ratio, which is $3x$:

$\text{Age of youngest boy}=3\times 5=15\text{years}$

Hence, the age of the youngest boy is 15 years.