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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


Team Careers360 10th Jan, 2024
Answer (1)
Team Careers360 14th Jan, 2024

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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