Question

A man has some hens and some cows, 40 in numbers. His son counts the total number of legs they have and finds the total number of legs is 110. How many hens and how many cows does the man have?

Answer 1

Given:

Total number of cows and hens are 40.

Total number of legs are 110.

Let the number of hens be x.

Then according to the question the number of cows will be $40-\mathrm{x}$.

We can write,

Total number of legs as sum of 2 times the number of hens and 4 times the number of cows.

$\Rightarrow$Total number of legs$=2x+4(40-x)$

$\Rightarrow$Total number of legs $=2x+160-4x$

$\Rightarrow$Total number of legs$=160-2x$

By using the given value of total number of legs as 110, we get,

$$\begin{gathered} \Rightarrow 110=160-2x \\ \Rightarrow 2x=160-110 \\ \Rightarrow x=50/2 \\ \Rightarrow x=25 \end{gathered}$$

Hence, the number of hens are 25 and the number of cows are $(40-25)$ i.e.; 15.