# How many days can you feed the people in a shelter if there is food for 160 people for 40 days but after 15 days 40 more people come?

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Let us say that we have x amount of food enough to feed 160 people for 40 days.

==> 160 needs x for 40 days.

==> Ater 15 days:

==> 160 people consumed (15/40)*x =(3/8)x of the food.

Then what we have left is x- 3/8x = (5/8)x

==> 160 needs (5/8)x for 25 days

==> 200 needs (5/8)x for y days

==> for 1 day: 160 people = (5/8)*x /25

200 people = (5/8)*x/y

==> 160*(5/8)*x/y = 200*(5/8)*x/ 25

==> 160/y = 200/25

==> 160/y = 8

==> y =160/8 = 20

==> 200 needs (5/8)*x for 20 days

There are 160 people in the shelter. They can be fed for 40 days.

Let each person use 1 bag of food in a day.

Initially the number of bags is 160*40 = 6400.

In 15 days 160 people use 160*15 = 2400 bags of food.

The number of bags of food left is 6400 - 2400= 4000.

As 40 more people join them now, the number of people now becomes 200. But the number of bags is 4000.

So these can be used to feed them for another for 4000 / 200 = 20 days.

**In all, the people can be fed for 15 + 20 = 35 days.**

Given that the food stock is enough 40 days for 160 people.

Let consider food for a man for one day as 1 unit of 'food manday' or "fmd..

So food stockin the beginning is 160*40 fmd'.

After 15 days the food units consumed by 160 men = 160*15 fmd.

Therefore after 15 days remaining food = (160*40-160*15)fmd = 4000 fmd

Number additional people after 15 days = 40.

So the total number of people daly to be fed after 15 days = 160+40 = 200.

Therefore the daily consumtion of food by 200 people every day from the 16th day onwards= 200fmd.

Therefore the number of days the remaining food of 4000fmdis consumed by 200 people = 4000fmd/200fmd = 20days.

So we can feed the remaining stock of 4000fmd for 200 people for 20 days