Question

A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. Find the number of those who attended the picnic.

Answer 1

Let $x$ be the number of persons.

Amount spend $=₹96$

So the contribution of each person $=\frac{96}{x}$

Since four persons did not turn up,

$\Rightarrow$contribution of each person $=\frac{96}{x-4}$

Others had to contribute$₹4$ extra.

So we can write $\Rightarrow \frac{96}{x-4}-\frac{96}{x}=4$

$\Rightarrow \frac{1}{x-4}-\frac{1}{x}=\frac{4}{96}$

$\Rightarrow \frac{1}{x-4}-\frac{1}{x}=\frac{1}{24}$

$\Rightarrow \frac{x-(x-4)}{(x-4)x}=\frac{1}{24}$

$\Rightarrow \frac{x-x+4}{(x-4)x}=\frac{1}{24}$

$\Rightarrow \frac{4}{x^2-4x}=\frac{1}{24}$

$\Rightarrow x^2-4x=96$

$\Rightarrow x^2-4x-96=0$

$\Rightarrow (x-12)(x+8)=0$

$\Rightarrow x-12=0$ or $x+8=0$

$\Rightarrow x=12$ or $x=-8$ (neglect)

So, $x=12$

Number of those who attended the picnic$=x-4=12-4=8$

Thus, the number of those who attended the picnic $=8$