Question

In a care van, in addition to 50 hens, there are 45 goats and 8 camels with some keepers. If the total number of feet is 224 more than the total number of heads, find the number of keepers.
(a) 15
(b) 16
(c) 17
(d) 19

Answer 1

Hint: Let the number of keepers be K. Calculate the number of feet and total number of heads using the information that
Number of feet of 1 hen = 2
Number of feet of 1 goat = 4
Number of feet of 1 camel = 4
Number of feet of 1 keeper = 2
Then form an equation with the help of information that the number of feet is 224 more than the number of heads and solve the equation.

Complete step-by-step answer:
Let the number of keepers in the care van be Know we calculate the total number of heads. Let the total number of heads in the care van be H.
We know that each animal or person has only one head. So the number of heads is nothing but the number of animals and people in the care van.
So,
 $\begin{align}
  & H=\underbrace{50}_{hens}+\underbrace{45}_{goats}+\underbrace{8}_{camels}+\underbrace{K}_{keepers} \\
 & \,\,\,\,\,\,=103+K\,\,\,\,\,\,\,\,\cdot \cdot \cdot (\text{i}) \\
\end{align}$
Now we have to calculate the number of feet. Let the number of feet be F.
We know that
Number of feet of 1 hen = 2
Number of feet of 1 goat = 4
Number of feet of 1 camel = 4
Number of feet of 1 keeper = 2
So,
$\begin{align}
  & F=50\times 2+45\times 4+8\times 4+K\times 2 \\
 & \Rightarrow F=100+180+32+2K \\
 & \Rightarrow F=312+2K\,\,\,\,\,\,\cdot \cdot \cdot \text{(ii)} \\
\end{align}$
Now it is given that the number of feet is 224 more than the number of heads.
So,
$F=H+224$
Putting the value of F and H from equation (i) and (ii) we get
$\begin{align}
  & 312+2K=103+K+224 \\
 & \Rightarrow K=327-312 \\
 & \Rightarrow K=15 \\
\end{align}$
So, the number of keepers is 15.
Hence option (a) is correct.

Note: This question is requiring the number of feet of each animal. If one doesn’t know the number of feet then this question cannot be solved. Use the concept of features of each living being as different creatures are attributed with different legs, feet etc.