A batsman scores 180 runs in an innings, including 11 boundaries and 8 sixes; what percentage of his total score does he make by running between the wickets?

Introduction / Context:
This question comes from cricket based percentage problems in aptitude exams. A batsman score consists of runs from boundaries and sixes plus runs made by physically running between the wickets. The goal is to calculate the proportion of his total score that comes from running. This type of problem checks understanding of decomposition of a total into parts and then converting one part into a percentage of the whole.

Given Data / Assumptions:

• Total runs scored by the batsman = 180.
• He hits 11 boundaries, each boundary gives 4 runs.
• He hits 8 sixes, each six gives 6 runs.
• All remaining runs are made by running between the wickets.
• We must find the percentage of total runs that come from running.

Concept / Approach:
The total score is the sum of runs scored via boundaries, sixes, and running. We first compute the runs earned from boundaries and from sixes. The difference between the total score and this sum gives the runs made by running between the wickets. Then, to find the percentage contribution of running, we divide these running runs by total runs and multiply by 100. This is an application of the basic percentage formula in a sports context.

Step-by-Step Solution:
Runs from boundaries = number of boundaries * 4 = 11 * 4 = 44.Runs from sixes = number of sixes * 6 = 8 * 6 = 48.Total runs from boundaries and sixes = 44 + 48 = 92.Total score is 180 runs.Runs made by running between wickets = total runs - runs from boundaries and sixes = 180 - 92 = 88.Now compute the percentage of runs scored by running: (88 / 180) * 100.88 / 180 simplifies to 0.4888 recurring approximately.Multiplying by 100 gives approximately 48.88%.

Verification / Alternative check:
To verify quickly, note that half of 180 is 90, so 88 is very close to half of his total runs. Therefore, the percentage should be very close to 50%. Among the options, 48.88% is just under 50% and matches our calculated value. This sanity check with approximate values helps confirm that the detailed arithmetic performed is correct and no calculation step has been missed or misapplied.

Why Other Options Are Wrong:
51.42% and 62.45% are both above 50%, implying that more than half or much more than half of the runs are scored by running, which is inconsistent with 88 being slightly less than 90.

47.32% is somewhat close to 48.88% but still not equal to the accurate ratio of 88 out of 180, which is exactly 0.4888 recurring.

Common Pitfalls:
Some students mistakenly add up 11 and 8 to get 19 and then treat 19 as runs instead of boundaries or sixes. Others forget to multiply by 4 and 6 respectively or miscalculate the total runs from boundaries and sixes. Another common error is to divide the total by the running runs instead of running runs by total. Always clearly separate each contribution to the total score and double check the arithmetic for the multiplication and subtraction steps before converting to a percentage.

Final Answer:
The batsman scores 48.88% of his total runs by running between the wickets.