In a cricket match Kumble took three wickets less then twice the number of wickets taken by srinath . The product of the number of wickets taken by these two is 20 , then the number of wickets taken by Kumble is

Options

A. 4
B. 5
C. 10
D. 12

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the Variables
Let the number of wickets taken by Srinath be \( x \). According to the problem, Kumble took three wickets less than twice the number of wickets taken by Srinath. Therefore, we can express the number of wickets taken by Kumble as:
\[ K = 2x - 3 \]

### Step 2: Set Up the Equation
We know that the product of the number of wickets taken by Srinath and Kumble is 20. Thus, we can write the equation:
\[ x(2x - 3) = 20 \]

### Step 3: Expand the Equation
Expanding the left side of the equation gives us:
\[ 2x^2 - 3x = 20 \]

### Step 4: Rearrange the Equation
To form a standard quadratic equation, we rearrange the equation:
\[ 2x^2 - 3x - 20 = 0 \]

### Step 5: Factor the Quadratic Equation
Now, we need to factor the quadratic equation. We look for two numbers that multiply to \( 2 \times -20 = -40 \) and add up to \( -3 \). The numbers that fit this are \( -8 \) and \( 5 \). Thus, we can rewrite the equation as:
\[ 2x^2 - 8x + 5x - 20 = 0 \]

### Step 6: Group the Terms
Now we group the terms:
\[ (2x^2 - 8x) + (5x - 20) = 0 \]

### Step 7: Factor by Grouping
Factoring out the common terms gives us:
\[ 2x(x - 4) + 5(x - 4) = 0 \]
This can be factored further:
\[ (2x + 5)(x - 4) = 0 \]

### Step 8: Solve for \( x \)
Setting each factor to zero gives us:
1. \( 2x + 5 = 0 \) → \( x = -\frac{5}{2} \) (not valid since wickets cannot be negative)
2. \( x - 4 = 0 \) → \( x = 4 \)

### Step 9: Find Kumble's Wickets
Now that we have \( x = 4 \) (the number of wickets taken by Srinath), we can find the number of wickets taken by Kumble:
\[ K = 2x - 3 = 2(4) - 3 = 8 - 3 = 5 \]

### Final Answer
The number of wickets taken by Kumble is \( 5 \).

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