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. The number of those who attended the picnic was

8

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12

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16

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24

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Solution

The correct option is D $8$
Let the number of persons be $x$ . Then,
$\frac{96}{x - 4} - \frac{96}{x} = 4 \Leftrightarrow \frac{1}{x - 4} - \frac{1}{x} = \frac{4}{96} \Leftrightarrow \frac{x - (x - 4)}{x (x - 4)} = \frac{1}{24}$
$\Leftrightarrow x^{2} - 4 x - 96 = 0 \Leftrightarrow (x - 12) (x + 8) = 0 \Leftrightarrow x = 12$
So, required number $= x - 4 = 8$ .

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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. The number of those who attended the picnic was

The correct option is D 8Let the number of persons be x. Then,96x−4−96x=4⇔1x−4−1x=496⇔x−(x−4)x(x−4)=124 ⇔x2−4x−96=0⇔(x−12)(x+8)=0⇔x=12So, required number =x−4=8.

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. The number of those who attended the picnic was