Question

A number of friends decided to go on a picnic and planned to spend Rs960 on food. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs40 each extra. The number of those who attended the picnic was
(a) 8
(b) 12
(c) 16
(d) 24

Answer 1

Hint:Let us assume that the total number of friends be ‘x’, then each person was $\dfrac{960}{x}$. Also, contribution of each friend after 4 friends leave = $\dfrac{960}{\left( x-4 \right)}$, so, we get an equation as according to the question as $\dfrac{960}{x-4}-\dfrac{960}{x}=40$. Now, we will solve the equation to find x.

Complete step-by-step answer:
It is given in the question that a number of friends decided to go on a picnic and planned to spend Rs960 on food. Four of them left the group, as a result the remaining one’s had to contribute Rs.40 each extra. Then, we have to find the number of friends who attended the picnic.
Let us first assume that the total number of friends decided to go on a picnic be x. Also, it is given that they will spend Rs960 on food. Accordingly, each member of the group has to contribute $\dfrac{Rs960}{x}$.
Now, it is given that 4 friends out of them left out and as a result, each one left had to pay an extra amount of Rs40 to meet the Rs960 value. Therefore the contribution per person would be $\dfrac{Rs960}{x-4}$.
Therefore, according to the question we get the following relation $\dfrac{960}{x-4}-\dfrac{960}{x}=40$. Solving this, we get
$\dfrac{960x-960\left( x-4 \right)}{x\left( x-4 \right)}=40$, solving further, we get
$960x-960x+3840=40x\left( x-4 \right)$, that is,
$3840=40{{x}^{2}}-160x$, rearranging the equation to get
$40{{x}^{2}}-160x-3840=0$, dividing the whole equation by 40, we get,
${{x}^{2}}-4x-96=0$, solving the equation by splitting the middle term, we get
${{x}^{2}}-12x+8x-96=0$, taking $x-12$ factor as common, we get,
$x\left( x-12 \right)+8\left( x-12 \right)=0$, that is,
$\left( x-12 \right)\left( x+8 \right)=0$, therefore ,we get values of x as $x=12,-8$.
Since, the number of members in a group cannot be negative, we get $x=12$ as the total number of group members.
Therefore, the total members who went to the picnic were $12-4=8$, that is option a) is the correct answer.

Note: The calculation is quite long and because of this the chance of error while solving is also very high. Usually students tend to make wrong equations due to not understanding the problem equation clearly. Thus, it is recommended to make the equation carefully and solve it carefully, avoiding the calculation mistakes.