# math

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if a camp has food to last for 25 days but after 10 days 150 people went back from the camp now the food lasts for 30 days. Answer how many people were present at beginning

• math -

There were 300 people. Consider number of people to be 'x' and total food to be 1 (or 100%, whichever you like).

Now, 'x' people eat 1 food in 25 days;
or, 25x people eat 1 food in 1 day______(eqn. 1)

1 food is eaten in 25 days;
or, 1/25 food is eaten in 1 day;
or, 10/25 food is eaten in 10 days (reduce the fractions).

So total number of people consume 10/25 food in 10 days. Remaining food is 1-(10/25) = 15/25.

That means,
x-150 people consume 15/25 food in 30 days.
or, 30(x-150) people consume 15/25 food in 1 day;
or, (25/15)*30(x-150) people consume 1 food in 1 day______(eqn. 2)

Eqn. 1 and 2 have equal quantity of food consumed in equal number of days. So the number of people must be equal, i.e.,

(25/15)*30(x-150) = 25x

Solve this, find the value of x (you should get 300). This is the number of people in the beginning.

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