The average age of the boys in a class is 12 years. The average age of the girls in the class is 11 years. There are 50% more girls than boys in the class. Which one of the following is the average age of the class (in years)?
11.2 years
11.4 years
11.6 years
11.8 years
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2020
Average age of boys ($A_B$) = 12 years.
Average age of girls ($A_G$) = 11 years.
$N_G$ is 50% more than $N_B$, so $N_G = N_B + 0.50 N_B = 1.5 N_B$.
The total sum of ages of boys is $N_B \times A_B = 12N_B$.
The total sum of ages of girls is $N_G \times A_G = 11N_G = 11(1.5N_B) = 16.5N_B$.
The total sum of ages in the class is $12N_B + 16.5N_B = 28.5N_B$.
The total number of students is $N_B + N_G = N_B + 1.5N_B = 2.5N_B$.
The average age of the class is $\frac{\text{Total sum of ages}}{\text{Total number of students}} = \frac{28.5N_B}{2.5N_B} = \frac{28.5}{2.5} = \frac{285}{25}$.
$\frac{285}{25} = \frac{57 \times 5}{5 \times 5} = \frac{57}{5} = 11.4$.
The average age of the class is 11.4 years.