Question

In a cricket match, Anil took one wicket less than twice the number of wickets taken by Ravi. lf the product of the number of wickets taken by them is $15$, the number of wickets taken by Anil and Ravi are

• A. $5,3$
• B. $3,5$
• C. $2,6$
• D. $7,9$

Answer 1

The correct option is A $5,3$

Let the number of wickets taken by Ravi be $r$.
Let the number of wickets taken by Anil be $a$.
Then
$ar=15$ ...(i)
And
$a=2r-1$...(ii)
Substituting the expression for $a$ in (i),
$r(2r-1)=15$
$2r^2-r=15$
$2r^2-r-15=0$
$2r^2-6r+5r-15=0$
$2r(r-3)+5(r-3)=0$
$(2r+5)(r-3)=0$
$r=\frac{-5}{2}$ and $r=3$.
Since the number of wickets taken cannot be negative, hence
$r=3$.
Thus
$a\left(r\right)=15$
$a\left(3\right)=15$
$a=5$.
Hence Anil took $5$ wickets while Ravi took $3$.