Question

In a school, 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 of the number of girls are also below 10 years. If the number of students of age 10 or more years is 260, then the number of boys in the school is:

• A. 280
• B. 300
• C. 234
• D. 312

Answer 1

Answer:

B. 300

Given:

No. of students who are girls = $\frac{3}{8}$ of the total no. of students.

No. of students who are boys = $\frac{5}{8}$ of the total no. of students.

No. of boys below 10 years = $\frac{1}{3}$ of the total no. of boys.

No. of boys above 10 years = $\frac{2}{3}$ of the total no. of boys.

No. of girls below 10 years = $\frac{2}{3}$ of the total no. of girls.

No. of girls above 10 years = $\frac{1}{3}$ of the total no. of girls.

No. of students with age 10 or above 10 years = 260

Calculation:

Let the total no. of students x

No. of students who are girls = ${3}{8}$ of x = $\frac{3x}{8}$

No. of students who are boys = $\frac{5}{8}$ of x = $\frac{5x}{8}$

According to the question,

⇒ Total students with age 10 or above = 260

⇒ No. of boys above 10 years + No. of girls above 10 years = 260

$⇒\frac{2}{3}of\frac{5x}{8}+\frac{1}{3}of\frac{3x}{8}=260$

$⇒\frac{5x}{12}+\frac{x}{8}=260$

$⇒\frac{(10x + 3x)}{24}=260$

$⇒\frac{13x}{24}=260$

 

∴ x = 480 → Total no. of students in the school

∴ Total no. of boys in the school = $\frac{5x}{8}=\frac{5}{8}\times{480}=300$.