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In a scout camp, there is food provision for \(300\) cadets for \(42\) days. If \(50\) more persons join the camp, for how many days will the provision last?
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Question

In a scout camp, there is food provision for \(300\) cadets for \(42\) days. If \(50\) more persons join the camp, for how many days will the provision last?

Answer

More the persons, the sooner would be the food provision exhausted. So, this is this case number of persons are inversely proportional to the food provision.
Let the provision last for \(x\) days.
\(\because\) Total food provision \(=\)Number of cadets \(\times \) Number of days.
We know that provision is same.
So, \(300\times 42=(300+50)\times x\)
\(300\times 42=350\times x\)
\(\frac {300\times 42}{350}=x\)
\(x=36\)days
Hence, number of days for which the provision will last when \(50\) more persons join are \(36\)days.
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