A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

### Concept & Formula This is a straightforward percentage share problem. To find the percentage of runs scored by running, we first need to determine the absolute number of runs scored by running, and then express that as a percentage of the total score. $$ \text{Percentage} = \left( \frac{\text{Runs by Running}}{\text{Total Runs}} \right) \times 100 $$ ### Step-by-step Solution **Given:** Total runs = 110 Boundaries (4s) = 3 Sixes (6s) = 8 First, calculate the runs scored through boundaries and sixes: Runs from 4s = $ 3 \times 4 = 12 $ Runs from 6s = $ 8 \times 6 = 48 $ Total runs from hits = $ 12 + 48 = 60 $ Next, calculate the runs made by running between the wickets: Runs by running = Total runs - Runs from hits $$ = 110 - 60 = 50 $$ Now, calculate the required percentage: $$ \text{Percentage} = \left( \frac{50}{110} \right) \times 100 $$ $$ = \frac{500}{11} $$ Convert the improper fraction to a mixed number: $ 500 \div 11 = 45 $ with a remainder of 5. $$ = 45 \frac{5}{11}\% $$ ### Exam Strategy & Shortcut Focus on the fraction $ \frac{5}{11} $. You should memorize standard percentage fractions. $ \frac{1}{11} \approx 9.09\% $. Therefore, $ \frac{5}{11} = 5 \times 9.09\% = 45.45\% $. Looking at the options, $ 45 \frac{5}{11}\% $ matches 45.45% perfectly. This saves you from performing the manual mixed-fraction conversion. ### Common Pitfall A common error in exam pressure is calculating the percentage of runs scored by *boundaries* instead of running. Finding $ \frac{60}{110} \times 100 $ yields $ 54 \frac{6}{11}\% $ (Option C), which is a deliberate distractor. Always double-check what the final sentence is asking for. ### Final Answer **Therefore, the correct answer is $ 45 \frac{5}{11}\% $.**