Question

A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses’ back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there?

• A. 10
• B. 12
• C. 14
• D. 16

Hint:

In such problems, focus only on entities contributing to the count (here, legs on the ground). Riders’ legs are not counted, but their horses always are.

Answer 1

The Correct Option is C

Concept: Count only the legs touching the ground. Riders do not contribute their legs to the ground count, while walking men and all horses do. Step 1:Let total number of men = total number of horses = $x$.} Half of the men are riding $\Rightarrow \frac{x}{2}$ men are on horses.
Remaining $\frac{x}{2}$ men are walking.
Step 2:Count legs on the ground.}

• Each horse has 4 legs $\Rightarrow$ total horse legs = $4x$
• Walking men = $\frac{x}{2}$, each has 2 legs $\Rightarrow$ total = $2 \times \frac{x}{2} = x$

Total legs on ground: \[ 4x + x = 5x \]
Step 3:Form equation.} \[ 5x = 70 \Rightarrow x = 14 \] Final Answer: \[ {14} \]