Question

All students of 10th class planned a picnic. The entire package with food was of Rs $960$. But eight students failed to go and thus, the cost for each member increased by Rs $6$.
(i) How many students attended the picnic?
(ii) Find the total number of students in 10th class.

Answer 1

Let total number of students in class be $x.$

Let cost of food for each student be $y.$

$\therefore$ Total cost of food for $x$ students$:-$

$\Rightarrow x\times y=960$ .... $\left(1\right)$

So, now according to given condition when $8$ students fails to go on picnic and cost of food increases by $6$ for each student

$\therefore (x-8)(y+6)=960$.... $\left(2\right)$

Solving $\left(1\right)$ and $\left(2\right)$, we get

$6x-8y=48$

$\Rightarrow x=\frac{8y+48}{6}$

Substituting in $\left(1\right)$, we get

$\frac{8y+48}{6}\times y=960$

$\Rightarrow 8y^2+48y=960\times 6$

$\Rightarrow y^2+6y=720$

Solving this quadratic equation, we get

$y=24$, ignoring negative value since $y$ can't be negative

$\therefore x=40$

$\therefore$ Total number of students in class $=40$ $\to$ (Answer for $\left(ii\right)$)

Total number of students who attended picnic$=32$ $\to$ (Answer for $\left(i\right)$)