Question

There are several human beings and several cows in a village. One tenth of the humans have lost a leg. The total number of feet is 77. If anyone is chosen at random from the village, then the probability of not getting a cow is

• A. $\frac{1}{7}$
  
• B. $\frac{3}{5}$
  
• C. $\frac{5}{7}$
  
• D. $\frac{6}{7}$
  

Answer 1

The correct option is D $\frac{6}{7}$


Let the number of human beings be x and the number of cows be y.
$\therefore \text{Number of humans who have only 1 leg}=\frac{x}{10}$
$\Rightarrow \text{Number of humans having both legs}=1-\frac{x}{10}$
$=\frac{9x}{10}$
Since a human being has 2 feet and a cow has 4 feet.
According to the question:
$(\frac{x}{10}\times 1)+(\frac{9x}{10}\times 2)+(y\times 4)=77$
$\Rightarrow \frac{x}{10}+\frac{18x}{10}+4y=77$
$\Rightarrow 19x=770-40y$
Since, the number of human beings and cows can be only positive integer, the possible values of x and y, are 30 and 5, respectively.
Thus, the number of human beings is 30.
$\therefore \text{P(not getting a cow)}=\frac{\text{Outcomes of selecting a human}}{\text{Total number of outcomes}}$
$=\frac{30}{30+5}$
$=\frac{30}{35}$
$=\frac{6}{7}$
Hence, the correct answer is option (d).