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The stock of grain in a government warehouse lasts 30 days for 4000 people . How many days will it last for 6000 people ?

Answer
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Hint:- Find out the total stock in grain assuming the amount consumed by 1 person in 1 day. Use the concept of unitary method to find the total stock consumed by 4000 and 6000 people separately.

Complete step-by-step answer:
It has been given that 4000 people consume the stock of grain in a government warehouse in 30 days.
We will assume that 1 person can consume x food in 1 day
We can rewrite this as
1 person in 1 day consumes x food
Thus, 4000 people in 1 day consumes 4000X food
Again, 4000 people in 30 days consumes 4000x×30 food
From the above, we get the total food to be equal to 4000x×30
Now let us assume that 6000 people consume the total food in y days
Again,
1 person in 1 day consumes x food
Thus, 6000 people in 1 day consumes 6000×x food
Thus, 6000 people in y days can consume 6000×y×x food
From the above, we get the total food to be equal to 6000×y×x
Since the total food in the stock remains the same, we get
4000x×30=6000×y×x
Solving the above equation, we get
y=4000×306000y=20

Thus, 6000 people can consume the whole stock in 20 days.

Note:- In time and work we calculated and found the time required to complete a piece of work and also find work done in a given period of time. We know the amount of work done by a person varies directly with the time taken by him to complete the work.

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