Question

There are several human beings and several dogs in a room. One tenth of the humans have lost a leg. The total numbers of feet are $77$. Then the number of dogs is:

• A. Not determinable due to insufficient data
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (C)

$5$

Let there be $x$ human beings and $y$ dogs
Therefore, total legs $=2x+4y$
One tenth of $x$ human beings lost their legs
Thus, $2x+4y-\frac{x}{10}=77$
$\frac{19x}{10}+4y=77$
Both the terms, $\frac{19x}{10}$ and $4y$ must be natural numbers as they represent the number of legs of human beings and dogs respectively. Therefore, $x$ must be a multiple of $10$ for this condition to be satisfied.

By Hit and Trial Method,
when $x=10$
$4y=58$, which is not possible
when, $x=20$
$4y=39$ which is not possible
when, $x=30$
$4y=20$
$y=5$

when, $x=40$

$4y=1$, which is again not possible

Thus, there are $5$ dogs.
Hence, option $C$ is correct.