# 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!