Question : 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 who are below 14 years of age, and $\frac{2}{5}$ of the number of girls who 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:
Option 1: 1820
Option 2: 1290
Option 3: 1900
Option 4: 1920
Correct Answer: 1920
Solution :
Let $x$ be the total number of students in the school.
Number of girls = $\frac{5x}{12}$
Number of boys = $\frac{7x}{12}$
Number of boys who are below 14 years of age = $\frac{4}{7}×\frac{7x}{12}$ = $\frac{x}{3}$
Number of girls who are below 14 years of age = $\frac{3}{5}×\frac{5x}{12}$ = $\frac{x}{4}$
Number of students who are below 14 years of age = $\frac{x}{3}+\frac{x}{4}$
⇒ 1120 = $\frac{7x}{12}$
⇒ $x$ = $\frac{1120 × 12}{7}$
= 12 × 160
= 1920
Hence, the correct answer is 1920.
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