Based on the provided data concerning the tournament performance of six different players, answer the following questions: | Player | Matches Played | Run Average | Balls Faced | Strike Rate | |---|---|---|---|---| | A | 8 | — | — | 129.6 | | B | 20 | 81 | — | — | | C | — | 38 | 400 | 114 | | D | — | — | — | 72 | | E | 28 | 55 | 1280 | — | | F | — | — | — | 66 | Important Guidelines: 1. Strike Rate is calculated as (Total Runs / Balls Faced) * 100. 2. Every player batted in every match they played. 3. Hyphens (-) indicate missing data points that must be derived to solve the problems. Players D and F have a balls-faced ratio of $3 : 4$ respectively. By what percentage does the total run count of player F exceed the total run count of player D?

### Concept & Percentage Change The problem requires calculating the percentage by which one value exceeds another based on proportional variables. $$ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 $$ ### Step-by-Step Solution 1. **Assign Variables:** Let the total balls faced by D and F be $3x$ and $4x$, respectively. 2. **Calculate Runs for D:** - Strike Rate = 72 - Runs by D = $\frac{72}{100} \times 3x = 2.16x$ 3. **Calculate Runs for F:** - Strike Rate = 66 - Runs by F = $\frac{66}{100} \times 4x = 2.64x$ 4. **Determine the Difference:** - Excess runs by F = $2.64x - 2.16x = 0.48x$ 5. **Calculate the Percentage:** - Percentage More = $\left( \frac{0.48x}{2.16x} \right) \times 100$ - Simplify the fraction: $\frac{48}{216} = \frac{12}{54} = \frac{2}{9}$ - $\frac{2}{9} \times 100 = \frac{200}{9} = 22\frac{2}{9}\%$ ### Exam Strategy & Shortcut Skip the decimals by working directly with ratios. D's runs scale as $72 \times 3 = 216$. F's runs scale as $66 \times 4 = 264$. The difference is 48. $\frac{48}{216} = \frac{2}{9}$, which is instantly recognizable as $22.22\%$ or $22\frac{2}{9}\%$. ### Common Pitfall Dividing by F's runs ($2.64x$) instead of D's runs ($2.16x$) is a common error. Always divide by the "than" value (the baseline). ### Final Answer Therefore, the correct answer is **$22\frac{2}{9}$**.