Question

In a scout camp, there is a food provision for 300 cadets for 42 days. If 50 more people join the camp then after how many days will the provision be left.

Answer 1

Hint:- We had to only find the food consumed by each cadet in one day and the total food consumed in one day when there were 300 cadets and then find the food consumed by all cadets in one day when there were 50 more persons.

Complete step by step answer:
Let the total food provision be x.
So, as we know that when there were 300 cadets then the food lasted for 42 days.
So, food consumed by all 300 cadets in one day will be = \[\dfrac{x}{{42}}\]
And the food consumed by each cadet in one day will be = \[\dfrac{{{\text{Total food consumed in a day}}}}{{{\text{Total number of cadets}}}} = \dfrac{{\dfrac{x}{{42}}}}{{300}} = \dfrac{x}{{12600}}\]
Now when 50 more persons joined the camp then the total food consumed in a day will be = total food consumed in a day by 300 cadets + 50*(food consumed by each person in a day) = \[\dfrac{x}{{42}} + \left( {50 \times \dfrac{x}{{12600}}} \right) = \dfrac{x}{{42}} + \dfrac{x}{{252}} = \dfrac{x}{{36}}\]
Now as we had calculated above that when 50 more persons joined the camp then the food consumed by all the persons in a day = \[\dfrac{x}{{36}}\]
Now as we have assumed above that the total food provision is x.
So, number of days after which food last will be = \[\dfrac{{{\text{Total food provision available}}}}{{{\text{Food consumed in one day}}}} = \dfrac{x}{{\dfrac{x}{{36}}}} = 36\]days.
Hence, after 36 days food provision will end when 50 more persons join the camp.

Note:Whenever we come up with this type of problem then first, we had to assume the total food available as x. And after that we divide that by the number of days after food last to get the food consumed by all (300) cadets in a day. And then we divide that with the number of cadets to get the food consumed by a cadet in one day. After that total food consumed in a day will be the sum of food consume in a day when there were 300 cadets and 50*(food consumed by each cadet in a day). Then we divide the total food available with the total food consumed by all (350) persons in a day to get the required number of days after which food will last. This will be the easiest and efficient way to find the solution of the problem.