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
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.
To find out how many people were present at the beginning of the camp, we can set up an equation based on the information given.
Let's assume that "X" represents the number of people present at the beginning of the camp.
We are given that the camp has food to last for 25 days. After 10 days, 150 people went back from the camp. With this, we know that there were X - 150 people left at the camp after the 10 days.
It is also given that the remaining food is enough to last for 30 days. We can set up a proportion using the number of people and the number of days:
(X - 150) / 25 = X / 30
To solve this equation, we can cross-multiply:
30(X - 150) = 25X
Now, we can distribute and simplify the equation:
30X - 4500 = 25X
Combine like terms:
30X - 25X = 4500
5X = 4500
Divide both sides by 5:
X = 900
Therefore, there were 900 people present at the beginning of the camp.