A batsman scores 120 runs in an innings, including 3 boundaries and 8 sixes. What percentage of his total score does he make by running between the wickets?

Introduction / Context:
This question applies basic arithmetic and percentage concepts to a cricket scoring scenario. The batsman scores some runs through boundaries and sixes, and the remainder are scored by running between the wickets. You are asked to find the fraction of his total score contributed by running and express it as a percentage. Sports-based percentage questions like this are common in aptitude tests and help connect maths to real life contexts.

Given Data / Assumptions:

• Total runs scored by the batsman = 120.
• He hits 3 boundaries, each worth 4 runs.
• He hits 8 sixes, each worth 6 runs.
• The remaining runs are scored by running between the wickets.
• We must find the percentage of total runs that come from running.

Concept / Approach:
The steps are straightforward. First, calculate the runs scored from boundaries and from sixes separately. Then, add these to get total runs from hits to the fence or over it. Subtract this from the overall score to determine how many runs came from running between the wickets. Finally, express that running score as a percentage of the total score by using the formula (runs from running / total runs) * 100%.

Step-by-Step Solution:
Step 1: Total runs scored = 120.Step 2: Runs from boundaries (4 runs each) = 3 * 4 = 12 runs.Step 3: Runs from sixes (6 runs each) = 8 * 6 = 48 runs.Step 4: Total runs from boundaries and sixes combined = 12 + 48 = 60 runs.Step 5: Runs scored by running between the wickets = total runs - runs from boundaries and sixes = 120 - 60 = 60 runs.Step 6: Now compute the percentage of total runs scored by running = (runs by running / total runs) * 100%.Step 7: This is (60 / 120) * 100% = 0.5 * 100% = 50%.Step 8: Therefore, 50% of his total score is made by running between the wickets.

Verification / Alternative check:
We can see that in this particular innings, the batsman scores 60 runs by big hits and 60 runs by running. Since the total is 120, it is clear that half of his runs come from running and half from boundaries and sixes. Half of any total is 50%, so this confirms the percentage found by the detailed calculation. The symmetry in the numbers (60 runs from each source) makes the verification intuitive and convincing.

Why Other Options Are Wrong:
Option 40% would correspond to 48 runs from running, which would imply 72 runs from boundaries and sixes, but that contradicts the given hit counts. Option 45% would correspond to 54 running runs, again inconsistent with the remaining scoring pattern. Option 55% would require 66 runs by running and 54 from boundaries and sixes, which cannot occur with 3 boundaries and 8 sixes. Option 35% would mean only 42 runs by running, which is also impossible given the total and the scoring strokes. Only 50% matches the computed distribution of runs.

Common Pitfalls:
Some learners forget to multiply the number of boundaries and sixes by 4 and 6 respectively and instead mistakenly add the counts directly. Others may subtract incorrectly or compute the percentage using the wrong base (for example, dividing by the runs from hits instead of the total score). To avoid these issues, carefully calculate runs from each scoring mode, find the running runs by subtraction, and then use the standard percentage formula (part / whole) * 100% with the total score as the whole.

Final Answer:
The batsman scored 50% of his runs by running between the wickets.