Question

If a hen and a half can lay an egg and a half in a day and a half, then how much time is needed for three hens to lay three eggs?

Answer 1

Hint: In the given question, we have been asked to find the number of days in which 3 hens lay 3 eggs and it is given that a hen and a half can lay an egg and a half in a day and a half. First we will need to find a way at which a hen lays eggs in a day, then will easily calculate the number of days. Here, we can also observe that the number of hens and the eggs will get double but not the days so we can easily answer this question.

Complete step-by-step solution:
We have given that,
A hen and a half laid an egg and a half in a day and a half.
In simpler for,
One and half is equal to = $$1+{\displaystyle \frac{1}{2}}={\displaystyle \frac{3}{2}}=1.5$$
Thus,
If 1.5 hens lay 1.5 egg in 1.5 days.
The rate at which the hens lay eggs;
$${\displaystyle \frac{3}{2}}hens\times {\displaystyle \frac{3}{2}}days\times Rate={\displaystyle \frac{3}{2}}eggs$$
Multiply both the sides by$${\displaystyle \frac{2}{3}}$$, we get
$${\displaystyle \frac{2}{3}}({\displaystyle \frac{3}{2}}hens\times {\displaystyle \frac{3}{2}}days\times Rate)={\displaystyle \frac{2}{3}}\times {\displaystyle \frac{3}{2}}eggs$$
Simplifying the above, we will get
$$1hen\times 1day\times {\displaystyle \frac{2}{3}}Rate=1egg$$
Therefore,
$$\Rightarrow Rate={\displaystyle \frac{3}{2}}$$
Now,
3 hens lays 3 eggs in;
$$3hen\times Days\times {\displaystyle \frac{2}{3}}Rate=3egg$$
Solving the above we will get
$$Days\times 2=3\Rightarrow Days={\displaystyle \frac{3}{2}}=1{\displaystyle \frac{1}{2}}$$
Therefore,
3 hens lay three eggs in a day and a half i.e. 1.5 day.
Here,
We can also understand this by table;

Note	Hens	Eggs	Days
1.5 hens lay 1.5 egg in 1.5 days	1.5	1.5	1.5
Doubling the hens will double the eggs but not the days i.e.	3	3	1.5

Note: While solving this question, most of the people get the question wrong. The reason is that a hen and a half cannot lay an egg and half i.e. a hen and half cannot lay an egg and a hen cannot lay half of an egg. But here we don’t take this question in a practical sense, we will only need to solve the given question without thinking much of a reality or true sense in the given question.