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:As the stock of grain in a government warehouse lasts $30$ days for $4000$ people.Then let for $1$ person consume $x$ grains in $1$ day then, $4000$ people in $30$ days will consume $4000 \times 30x$.So we get the total food we get and now we can find for $6000$ people how much it lasts.

Complete step-by-step answer:
According to the question, the stock of grain in a government warehouse lasts $30$ days for $4000$ people and if the population is increased to $6000$ people, then how much will it last?
Let $1$ person consume $x$ grains in $1$ day
So we can write that
For $1$ day, $1$ person$ = x$ grains
Now for $4000$ people, total amount of grain requires$ = 4000x$ but this is only for $1$ day
But it is said that the stock lasts for $30$ days, then
$4000$ people requires $ = 4000x(30)$amount of grains for $30$ days
So total amount of grain in the government warehouse is $ = 4000x(30)$, which is $120000x$
Now if the population is increased to $6000$, then what we need to do is that first of all let us assume the number of days to consume $120000x$ stock of grains by $6000$ people be $y$
We assume that one person consumes $x$ grains
So $6000$ in one day will consume $ = 6000x$
And as we assume that it lasts for $y$ days
So $6000$ in $y$ day will consume $ = 6000xy$ amount of grains
And this is equal to the total stock being calculated.
$120000x = 6000xy$
$120x = 6xy$
$y = 20{\text{ days}}$
So $6000$ will consume the stock in $20{\text{ days}}$

Note:If $4000$ persons consume $x$ amount in $30$ days.Then $1$ person in $1$ day will consume $\dfrac{x}{{(4000)(30)}}$ amount.So $1$ person in $y$ day will consume $\dfrac{{xy}}{{(4000)(30)}}$ amount.Now $6000$ person in $y$ day will consume $\dfrac{{6000xy}}{{(4000)(30)}}$ amount.