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**Hint:**We will first write the number of meals we have for 4000 people for 30 days by multiplying both of these quantities. After that, we will divide the total number of meals by 6000 to get the answer.

**Complete step-by-step solution:**

We are given that the stock of grain in a government warehouse lasts 30 days for 4000 people.

So, this means that we have:-

$ \Rightarrow $ Number of meals = \[4000 \times 30\]

Simplifying the RHS of the above equation to get:-

$ \Rightarrow $ Number of meals = 120000

So, we totally have 120000 meals.

If we need to distribute them for 6000 people, we will get:-

$ \Rightarrow $ Number of days 6000 people can have meal = $\dfrac{{120000}}{{6000}}$

Simplifying the numerator of RHS by cutting out the zeroes common of the above equation to get:-

$ \Rightarrow $ Number of days 6000 people can have meal = $\dfrac{{120}}{6}$

Simplifying the RHS of the above equation further to get:-

$ \Rightarrow $ Number of days 6000 people can have a meal = 20.

$\therefore $ the grain will last for 20 days for 6000 people.

**Hence, the answer is 20 days.**

**Note:**The students must notice that we first calculated the total meals we have and then divided it by the number of people to get the number of days.

Let us understand one more alternate method for the same question:-

We will use proportion methods to find the number of days the grain will last.

Since, we know that the grain is constant.

Let 1 person consume x meals a day.

So, 4000 people will consume 4000x meals a day.

Since, we have the grain for 30 days for 4000 people.

Therefore, we have $4000x \times 30 = 120000x$ meals overall.

Now, for 6000 people this remains constant because we have this much grain only.

Now, 6000 people will also consume x meal per person per day, therefore, 6000x meals.

Let us say they can consume it for y days.

Therefore, 6000 people will consume 6000xy meals.

$\therefore 6000xy = 120000x$

Now, on solving the above equation, we will get:-

$ \Rightarrow y = 20$

Hence, the answer is 20 days.

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