# Puzzle on Hen and Egg

## Puzzle on A Hen and An Egg

This is a hen and an egg puzzle.The premise and objective is given below.

Premise  – A hen and a half hen lay one and a half eggs in one and a half-day.

Objective – 1. How many eggs does one hen lay in one day?
2. Also, find how many hens will lay one dozen eggs in 6 days?

### Solution of the Puzzle

Let us look at the solution for the given puzzle. According to the given question,

1.5 hens are laying 1.5 eggs in 1.5 days. Considering this we can form the given equation :

$1\frac{1}{2} \: Hens \times 1\frac{1}{2} \: Days \times r = 1\frac{1}{2} \: Eggs$ [ here, r= Rate]

= $\frac{3}{2} \: Hens \times \frac{3}{2} \: Days \times r = \frac{3}{2} \: Eggs$

Now, multiplying both the sides by $\frac{2}{3}$

= $1 \: Hen \times \frac{3}{2} \: Days \times r = 1 \: Eggs$

Now on solving the equation and multiplying it by $\frac{2}{3}$, we get :- r = $\frac{2}{3}$ of an egg per day.

Thus, one hen lays $\frac{2}{3}$ of an egg in one day.

Now as we know that the rate of laying eggs per day. So it is easier to find out the second objective. So the condition we are given with is eggs = 12 , days = 6 and let the hens be H.

So the equation for the given condition be :- $\frac{3}{2} \: Hens \times \frac{3}{2} \: Days \times r = \frac{3}{2} \: Eggs$

= $H \: Hens \times 6\: Days \times \frac{2}{3} = 12 \: Eggs$

On solving this equation, we obtain H = 3

Conclusion – Therefore, 3 hens will produce 12 eggs in 6 days.