Question

$A$ fires $5$ shots to $B$'s $3$ but $A$ kills only once in $3$ shots while $B$ kills once in $2$ shots. When $B$ has missed $27$ times, $A$ has killed

• A. $30$ birds
• B. $60$ birds
• C. $72$ birds
• D. $90$ birds

Answer 1

The correct option is A $30$ birds

Let the total number of shots be $x$. Then,
Shots fired by $A=\frac{5}{8}x$; Shots fired by $B=\frac{3}{8}x$.
Killing shots by $A=\frac{1}{3}$ of $\frac{5}{8}x=\frac{5x}{24}$;
Shots missed by $B=\frac{1}{2}$ of $\frac{3}{8}x=\frac{3x}{16}$.
$\therefore$ $\frac{3x}{16}=27$ or $x=\left(\frac{27\times 16}{3}\right)=144$.
Birds killed by $A=\frac{5x}{24}=(\frac{5}{24}\times 144)=30$.