Laying Egg's -Math Riddle

Answer: Two dozen (24) 

Explanation :  

Certainly! Let's break down the explanation in a mathematical manner.

The original statement says, "If a hen and a half lay an egg and a half in a day and a half, how many eggs will half a dozen hens lay in half a dozen days?"

We've already established that one hen lays one egg in one day. To represent this, we can use the following equation:

1 hen = 1 egg/day

Now, let's introduce the concept of time and the number of hens increasing four-fold:

Number of hens increased four-fold: 1.5 hens * 4 = 6 hens
Time available increased four-fold: 1.5 days * 4 = 6 days
With these increases, we want to find out how many eggs the 6 hens will lay in 6 days. To do this, we can set up a proportion based on the original information:

(1.5 hens / 1.5 days) = (6 hens / 6 days)

Now, to determine the number of eggs laid by the 6 hens in 6 days, we can calculate it as follows:

6 hens/day * 6 days = 36 eggs

So, when we increase both the number of hens and the amount of time available four-fold, the number of eggs increases 16 times:

16 * 1.5 (original rate) = 24 eggs

This equation illustrates how the number of eggs increases when both the number of hens and the time available are increased four-fold.