Question

Pupils of ${10}^{th}$ standard of a school had arranged a function at a total cost of Rs. $1,000$ which was to be shared equally among them. Since $10$ of them failed to join the function each of them had to pay Rs. $5$ more. Find the number of pupils in the class.

Answer 1

Let the number of pupils $=x$

Total cost $=$ Rs. $1000$

Each share $=$ Rs. $\frac{1000}{x}$

If $10$ of them are failed to join the function then number of pupils joined $=x-10$

Total cost $=$ Rs. $1000$

Each share $=$ Rs. $\frac{1000}{x-10}$

Each would have to pay Rs. $5$ more

$\frac{1000}{x-10}-\frac{1000}{x}=5$

$\frac{1000x-1000(x-10)}{x(x-10)}=5$

$1000x-1000x+10000=5x^2-50x$

$5x^2-50x-10000=0$

Divide by $5$

$x^2-10x-2000=0$

$\Rightarrow x^2-50x+40x-2000=0$

$\Rightarrow x(x-50)+40(x-50)=0$

$\Rightarrow (x-50)(x+40)=0$

$\Rightarrow x=50,-40$

$\therefore x=50$

Number of pupils of the class $=50$.