Question

The average age of boys in the class is twice the number of girls in the class. If the ratio of the boys and girls in the class of 36 be 5:1, what is the total age of the boys in the class.
A. 420 years
B. 196 years
C. 490 years
D. 360 years

Answer 1

Hint: First let the number of boys be $5x$ and let the number of girls be $x$ as the ratio of boys and girls is 5:1. Then, use the given condition to form an equation and solve it for the value of $x$. Substitute the value of $x$ to find the total number of girls and boys. Then, apply the formula of average to find the sum of total ages of the boys in the class.

Complete step-by-step answer:
We are given that the ratio of boys and girls in a class is 5:1.
So, let the number of boys be $5x$ and let the number of girls be $x$.
Also, it is given that the total number of students in the class is 36.
Thus, we can say that
 $
  x + 5x = 36 \\
  6x = 36 \\
  x = 6 \\
$
Substitute $x = 6$ to find the number of boys and number of girls in the class.
There are $5\left( 6 \right) = 30$ boys in the class and 6 girls in the class.
We are given that the average age of boys in the class is twice the number of girls in the class.
Then, the average age of boys is $2\left( 6 \right) = 12$.
As, we know that average is calculated as, $\dfrac{{{\text{Sum of observations}}}}{{{\text{number of observations}}}}$
Therefore, sum of all ages of boys is given as, $12 \times 30 = 360{\text{ years}}$
Hence, option D is correct.

Note: Ratio is used to compare things of the same kind. When two numbers are written in a ratio, it means that one number is expressed as the fraction of the other number. Also, the formula for the calculation of average is given by $\dfrac{{{\text{Sum of observations}}}}{{{\text{number of observations}}}}$