Question

300 apples are distributed among a certain number of boys of a class. Had there been 10 more boys, each would have received one apple less. Find the number of boys in the class.

Answer 1

Please see the attachment

Answer 2

Let the original number of students be x

Number of apples received by each student = $\sf{\frac{300}{x}}$

Increased number of students = x + 10

Number of apples received by each student = $\sf{\frac{300}{x+10}}$

A/C,

$\sf\red{\frac{300}{x} - \frac{300}{x + 10} = }1$

$\longrightarrow$$\sf\red{300x + 3000 - 300x = x(x + 10)}$

$\longrightarrow$$\sf\red{ {x}^{2} + 10x - 3000 = 0}$

$\longrightarrow$$\sf\red{(x - 50)(x + 60) = 0}$

$\longrightarrow$$\sf\red{x = 50 \: or \: x = - 60}$

As the number of students cannot be negative, x ≠ -60 ,so x = 50

Hence, the original number of students = 50.