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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.


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Solution

Let x be the number of persons.

Amount spend =96

So the contribution of each person =96x

Since four persons did not turn up,

contribution of each person =96x-4

Others had to contribute4 extra.

So we can write 96x-4-96x=4

1x-4-1x=496

1x-4-1x=124

x-(x-4)(x-4)x=124

x-x+4(x-4)x=124

4x2-4x=124

x2-4x=96

x2-4x-96=0

(x-12)(x+8)=0

x-12=0 or x+8=0

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


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