Question

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

Answer 1

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 $4000x\times 30$ food
From the above, we get the total food to be equal to $4000x\times 30$
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 $6000\times x$ food
Thus, 6000 people in $y$ days can consume $6000\times y\times x$ food
From the above, we get the total food to be equal to $6000\times y\times x$
Since the total food in the stock remains the same, we get
$4000x\times 30=6000\times y\times x$
Solving the above equation, we get
$\begin{array}{l}y={\displaystyle \frac{4000\times 30}{6000}}\\ \Rightarrow y=20\end{array}$

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.