Question

In a cricket match against Sri Lanka, Sehwag took one wicket less than twice the number of wickets taken by Unmukt. If the product of the number of wickets taken by these two is $15$ . Find the number of wickets taken by each?

Answer 1

Hint: We will apply the method of factorization where two values of the variables will come out of which we have to select one appropriate value.

Complete step by step solution:
In a cricket match against Sri Lanka, Sehwag took one wicket less than twice the number of wickets taken by Unmukt. If the product of the number of wickets taken by these two is $15$. We have to find the number of wickets taken by each.
Let ‘x’ be the number of wickets taken by Unmukt.
As Sehwag took one wicket less than twice the number of wickets taken by Unmukt.
Hence the wickets taken by Sehwag $ = 2x - 1$
As it is given that product of the number of wickets taken by these two is $15$ .
Therefore $x \times \left( {2x - 1} \right) = 15$
$
  2{x^2} - x = 15 \\
  2{x^2} - x - 15 = 0 \\
  2{x^2} - 6x + 5x - 15 = 0 \\
  2x(x - 3) + 5(x - 3) = 0 \\
  \left( {2x + 5} \right)\left( {x - 3} \right) = 0 \\
$
Now we have two possible outcomes where either of the $\left( {2x + 5} \right)$ and $\left( {x - 3} \right)$ is equal to $0$ .
First we take $2x + 5 = 0$
$
  2x = - 5 \\
  x = \dfrac{{ - 5}}{2} \\
$
As negative value cannot be possible here so we take the second outcome.
Which is $x - 3 = 0$
$x - 3$
Now we will substitute the value of $x$ .
So the number of wickets taken by Unmukt $ = x$
And the no. of wickets taken by Sehwag $ = 2x - 1$
$
   = 2\left( 3 \right) - 1 \\
   = 5 \\
$
Note: At the end roughly check 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.