Question

In school X, the number of boys is more than that of the girls by 40%, In school Y, number of girls is more than that of boys by 50%. If 50% boys in school X is equal to 70% of girls in school Y, what is the ratio between the number of students of school X and School Y?

• A. 24 : 25
• B. 16 : 17
• C. 3 :4
• D. 36 :25

Answer 1

Answer: (A)

$In\text{school X}$
$\text{Let}\text{number of girls=x}$
$\text{number of boys=x+}\frac{40}{100}x$
$=\frac{7x}{5}$
$T\text{otal number of students in school X=x+}\frac{7x}{5}$
$=\frac{12x}{5}$
$In\text{school Y}$
$\text{let}\text{number of girls=y}$
$\text{number of boys=y+}\frac{50y}{100}$
$=\frac{3y}{2}$
$T\text{otal number of students in school Y= y+}\frac{3y}{2}$
$=\frac{5y}{2}$
$Given$
$50$
$\Rightarrow \frac{50}{100}\left(\frac{7x}{5}\right)=\frac{70}{100}\left(\frac{3y}{2}\right)$
$\Rightarrow \frac{7x}{10}=\frac{21y}{20}$
$x=\frac{3y}{2}$
$\text{Total number of students in school X=}\frac{12x}{5}$
$=\frac{12}{5}\left(\frac{3y}{2}\right)$
$=\frac{18y}{5}$
$T\text{otal number of students in school Y=}\frac{5y}{2}$
$Ratio\text{of number of students in school X to School Y}\text{=}\frac{\frac{18y}{5}}{\frac{5y}{2}}$
$=36:25$