Question

In a poultry farm, $50$ hens give $200$ eggs in $2$ days. In how many days will $20$ hens give $400$ eggs?

Answer 1

Hint:In the question, we are given a word problem related to ratio and proportions. These types of questions are to be done by unitary method. In this method, to solve the problems we are to find the value of a single unit of the product from the multiple values given. Then, use the value of the single unit to find the value of the required multiple value. The unitary method is very simple to solve many word problems based on the given conditions. So, in the given problem, we will use the unitary method to first find out the number of eggs given by one hen in one day.

Complete step by step answer:
It is given that, $50$ hens give $200$ eggs in $2$ days.
Now, by applying unitary method, we can write it as,
Number of eggs given by $50$ hens in $2$ days $ = 200$
So, number of eggs given by $1$ hen in $2$ days $ = \dfrac{{200}}{{50}} = 4$
Now, number of eggs given by $1$ hen in $1$ day $ = 2$
Therefore, we found the number of eggs $1$ hen gives in $1$ day.

Now, we will multiply or divide this result by a suitable number to get to the final answer.
So, number of eggs $20$hens will give in $1$day $ = 20 \times 2 = 40$
Now, we have to find the number of days in which $20$ hens will give $400$ eggs.
So, number of days in which $20$ hens will give $400$ eggs $ = \dfrac{{{\text{Total number of eggs}}}}{{{\text{Number of eggs in 1 day}}}}$ days
We know that $20$hens give $40$ eggs in one day. So, substituting the values of total number of eggs and number of eggs given by twenty hens in one day, we get,
$ \Rightarrow $ Number of days $ = \dfrac{{400}}{{40}}$
$ \therefore $Number of days $ = 10$

Therefore, $20$ hens will give $400$ eggs in $10$ days.

Note:The above problem can also be solved by comparing the ratios of the given case and the required case by assuming the number of days to be$x$. By comparing the ratios, we can do this in the following way,
$\dfrac{{{\text{(Number of eggs 50 hens give in 2 days)}}}}{{{\text{(Number of hen)}} \times {\text{(Number of days)}}}} = \dfrac{{{\text{(Number of eggs 20 hens give in x days)}}}}{{{\text{(Number of hen)}} \times {\text{(Number of days)}}}}$
This approach will also give the answer as $10$ days. But it's important to know the core concept of the unitary method behind the above formula.