A batswomman missed her century by four runs in an innings, in which the scoring shots in the form of sixes, fours, threes, twos and singles, were in the proportion 1:3:2:7:10. How many runs did she score in singles?

Options

A. 20
B. 16
C. 10
D. 12

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Problem
The batswoman missed her century by 4 runs, which means she scored 96 runs (100 - 4 = 96). The scoring shots are in the ratio of 1:3:2:7:10 for sixes, fours, threes, twos, and singles respectively.

### Step 2: Assign Variables
Let the common multiple for the ratio be \( x \). Therefore, we can express the number of scoring shots as follows:
- Sixes = \( 1x \)
- Fours = \( 3x \)
- Threes = \( 2x \)
- Twos = \( 7x \)
- Singles = \( 10x \)

### Step 3: Calculate Total Runs
Now, we calculate the total runs scored from each type of scoring shot:
- Runs from sixes = \( 6 \times 1x = 6x \)
- Runs from fours = \( 4 \times 3x = 12x \)
- Runs from threes = \( 3 \times 2x = 6x \)
- Runs from twos = \( 2 \times 7x = 14x \)
- Runs from singles = \( 1 \times 10x = 10x \)

Now, we add all these runs together:
\[ \text{Total Runs} = 6x + 12x + 6x + 14x + 10x = 48x \]

### Step 4: Set Up the Equation
Since we know the total runs scored is 96, we set up the equation:
\[ 48x = 96 \]

### Step 5: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 48:
\[ x = \frac{96}{48} = 2 \]

### Step 6: Calculate Runs from Singles
Now that we have \( x \), we can find the number of runs scored in singles:
\[ \text{Runs from singles} = 10x = 10 \times 2 = 20 \]

### Final Answer
The batswoman scored **20 runs in singles**.

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