Question

In a cricket match Anil took one wicket less than twice the number of wickets taken by Ravi. If the product of the number of wickets taken by them is $15$, the number wickets taken by Anil and Ravi are
A) 5,3
B) 3,5
C) 2,6
D) 7,9

Answer 1

Hint:In this problem we will make a simple two degree equation by the given data and solve it. First we will let the wickets taken by Ravi be $x$ and according to this we will make the equation about the wickets taken by Anil.

Complete step-by-step answer:
Let the number of wickets taken by Ravi is ‘$x$’.
So, it is given that the number of wickets taken by Anil is one wicket less than twice the number of wickets taken by Ravi.
So according to given situation, number of wickets taken by Anil is equal to $2x - 1$
Now, we have one more situation: the number of wickets taken by them is 15.
So, the product of Anil’s wicket and Ravi’s wicket is 15.
Now, according to the question required equation is
$\left( {2x - 1} \right) \times x = 15$
Mathematically
$2{x^2} - x = 15$
Mathematically
$
  2{x^2} - x - 15 = 0 \\
   \Rightarrow \left( {2x + 5} \right)\left( {x - 3} \right) = 0 \\
$
Now, apply zero product rule on the obtained factored equation, according to this rule, equate each factor to 0 and simplify for $x$.
Thus, we get
$\left( {2x + 5} \right) = 0$ or $\left( {x - 3} \right) = 0$
On solving the obtained equations, we get the values of $x$ as:
$3,{\text{& }}\,\dfrac{{ - 5}}{2}$
So, from this equation we get the value of $x$is $3,{\text{& }}\,\dfrac{{ - 5}}{2}$.
Here we will ignore negative values because the number of wickets cannot be negative.
So, the value of $x$ is 3 i.e. wickets taken by Ravi.
To find the number of wickets taken by Anil we have an equation $2x - 1$.
Put the value of $x - 3$ in this equation.
So, wickets taken by Anil is $2x - 1$
Mathematically, $2 \times 3 - 1$
$ = 5$
Hence, the wicket taken by Ravi is 3 and by Anil is 5.

Note:
At the end roughly check whether the product of the obtained value is equal to the given value or not. If equal then we had the right answer otherwise we have to check it once again.