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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?

Last updated date: 14th Sep 2024
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Hint: We have given that the stock of grain in a government warehouse lasts $30$ days for $4000$ people. Assume that one person consumes $x$ food in one day and simplify for $30$ days and $4000$ people. After that, let the number of days for $6000$ people be $y$ days and equate both of them.

Now let us assume that one person consumes $x$food in one day.
So, $1$ person $1$ day $\to $$x Now, for 4000 peoples 1 day\to$$4000x$
Also, for $4000$ peoples $30$ day$\to $$30\times 4000x Hence, total food =30\times 4000x ………… (1) So, let the number of days for 6000 people be ydays. Now, for 6000 peoples 1day\to$$6000x$
Also, for $6000$ peoples $y$day$\to$$6000xy$
Total food $=6000xy$ ………….. (2)
Now, equating (1) and (2), we get,
$\Rightarrow$ $30\times 4000x=6000xy$
Simplifying we get,
$\Rightarrow$ $\dfrac{30\times 4}{6}=y$
Again, simplifying we get,
$\Rightarrow$ $y=20$days
Therefore, the stock of grain in a government warehouse lasts $20$ days for $6000$ people.

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If $b$ is directly proportional to $a$ the equation is of the form $b=ka$ (where $k$ is a constant). Two variables are said to be in direct variation when the variables are related in such a way that the ratio of their values always remains the same. Direct variation means when one quantity changes, the other quantity also changes in direct proportion. Inverse variation is exactly opposite to this.