A Math Proportion Quiz Question

Question

If a hen and a half can lay an egg and a half in a day and a half, how many eggs can six hens lay in seven days?

Answer

Just write the sentences and you will get the answer!?

1.5 hen lays 1.5 eggs in 1.5 day

Now think.

Now four ” 1.5 hen ” [ that is 1.5*4 = 6 hens ] will lay four sets of “1.5 eggs” [ that is 1.5*4 = 6 eggs ] in just 1.5 day!!!

So, 6 hens lay 6 eggs in 1.5 day

In four “1.5 days” [ that is 1.5*4 = 6days], 6 hens would have laid a total of 4*6 = 24 eggs.

That is, 6 hens lay 24 eggs in 6 days

For the seventh day, it actually depends on what you assume proportional to what. Its a matter of interpretation and assumption. 3 possiblities only for assumption of proportionality, and each is given below.

Note : In each of the below, we will use the fact
“6 hens lay 24 eggs in 6 days” because it was
derived independent of any other extra assumptions.

Interpretation 1.(eggs are laid in proportional to the days discretely)
Using 6 hens lay 24 eggs in 6 days.
Now, In 6 days, 6 hens can lay 24 eggs. What about one day?
In one day, 6 hens can lay 4 eggs by assuming the eggs are layed in proportional to the days… i.e, 4 eggs per day from this statement. Thus in the seventh day, 4 eggs are produced by 6 hens. Hence total eggs = 24 + 4 = 28 eggs.

Interpretation 2.(eggs are proportional to the hen discretely)
If we assume the eggs are proportional to the hen.
then, from 6 hens lay 24 eggs in 6 days.
Then, 1 hen lays 4 eggs in 6 days. By further assumption that eggs and hen are proportional continously we get : one hen lays (7/6)*4 eggs in (7/6)*6 = 7 days;
Total eggs = 6* (7/6)*4 = 28 eggs.

Interpretation 3 ( hen is proportional to the days discretely )
This makes no sense, since the number of hens is NOT proportional to the days.

Both “possible” ways indicate the answer is total 28 eggs (Answer).

P/S:

If you see carefully, actually, interpretation 1 and 2 are the same because we cannot escape the fact that the eggs are laid out proportional to the hens!