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Some students planned a picnic. The total budget for food was ₹500, but $5$ of them failed to go and thus the cost of food for each student increased by ₹5. How many students attended the picnic?
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Sol. Let number of students who attended picnic be $x$.
A.T.Q.
$\frac{500}{x} - \frac{500}{x+5} = 5$
$\Rightarrow x^2 + 5x - 500 = 0$
$\Rightarrow (x + 25) (x - 20) = 0$
$x = -25, x = 20$
But number of students can't be negative.
Hence, $x = 20$
Therefore, number of students who attended picnic is $20$.
A.T.Q.
$\frac{500}{x} - \frac{500}{x+5} = 5$
$\Rightarrow x^2 + 5x - 500 = 0$
$\Rightarrow (x + 25) (x - 20) = 0$
$x = -25, x = 20$
But number of students can't be negative.
Hence, $x = 20$
Therefore, number of students who attended picnic is $20$.