In a school, $\frac{5}{12}$ of the number of students are girls and the rest are boys $\frac{4}{7}$ of the number of boys are below 14 years of age, and $\frac{2}{5}$ of the number of girls are 14 years or above 14 years of age. If the number of students below 14 years of age is 1120, then the total number of students in the school is:
Answer & explanation
Correct answer: option 4
Here,
Total no. of Girls = \(\frac{5a}{12}\)
Total no. of Boys = \(\frac{7a}{12}\)
⇒ Boys below 14 yrs of age = \(\frac{7a}{12}\) x \(\frac{4}{7}\) = \(\frac{a}{3}\)
⇒ Girls above 14 yrs of age = \(\frac{5a}{12}\) x \(\frac{2}{5}\) = \(\frac{a}{6}\)
⇒ Girls below 14 years of age = \(\frac{5a}{12}\) - \(\frac{a}{6}\) = \(\frac{a}{4}\)
⇒ Total no. of students below 14 years of age = \(\frac{a}{3}\) + \(\frac{a}{4}\) = \(\frac{7a}{12}\)
⇒ \(\frac{7a}{12}\) = 1120
⇒ a = 1920.
Therefore, total no. of students below 14 years of age are 1920.