Question

A farmer bought some laying hen. He split them into five equal group. Each group had double the number of red hens as white hens. Each group had half the number of red hens as speckled hens. There were 20 speckled hens in each group. How many hens did the farmer buy?

Answer 1

We have been given that there were 20 speckled hens in each group.

Now, we have been given that each group had half the number of red hens as speckled hens.

Therefore, in each group the number of red hens are

$20\times \frac{1}{2} =10$

Now, each group had double the number of red hens as white hens.

Number of white hens in each group is

$10\times \frac{1}{2} =5$

Hence, total number of hens is each group is 20+10+5 = 35

Now, he split them into five equal group.

Therefore, total number of hens the farmer bought is given by

$35 \times 5 \\ \\ =175$