In a temple, the average number of fruits offered in a week (7 days) is 75. The average number of fruits offered in six days excluding Tuesday is 72. How many fruits were offered on Tuesday?

Introduction / Context:
This problem is a straightforward average and total calculation scenario involving daily offerings at a temple. You are given the average number of fruits offered over a full week and a separate average over six days excluding Tuesday. From this, you must determine how many fruits were offered on Tuesday. Such problems help solidify comfort with translating between averages and totals in day wise contexts.

Given Data / Assumptions:
- The time period considered is a full week of 7 days.
- Average number of fruits offered per day over the full week = 75.
- So the total number of fruits offered over 7 days is 7 * 75.
- Average number of fruits offered over six days excluding Tuesday = 72.
- So the total number of fruits offered in those six days is 6 * 72.
- We must find the number of fruits offered on Tuesday alone.

Concept / Approach:
The guiding idea is that average equals total divided by number of days. First, compute the total fruits for the entire week using the weekly average. Next, compute the total for the six non Tuesday days using their average. The difference between the weekly total and the six day total gives the fruits offered on Tuesday, because Tuesday is the only day not included in the six day group.

Step-by-Step Solution:
Step 1: Total fruits offered over 7 days = weekly average * 7 = 75 * 7.Step 2: Compute 75 * 7 = 525 fruits.Step 3: Total fruits offered in six days excluding Tuesday = 6 * 72.Step 4: Compute 6 * 72 = 432 fruits.Step 5: The only day not included in this second total is Tuesday.Step 6: Fruits offered on Tuesday = total for full week - total for the six non Tuesday days.Step 7: Fruits offered on Tuesday = 525 - 432 = 93 fruits.Step 8: Therefore, 93 fruits were offered on Tuesday.

Verification / Alternative check:
We can verify by recalculating the averages. Suppose fruits offered on Tuesday are 93. The total for the entire week is 432 plus 93 = 525, and the average is 525 / 7 = 75, which matches the weekly average. The total for the six days excluding Tuesday is 432, and the average for those six days is 432 / 6 = 72, which matches the given six day average. This confirms that 93 is the correct number for Tuesday.

Why Other Options Are Wrong:
If Tuesday had 90, 92 or 72 fruits, then the recalculated weekly and six day averages would not match the given values simultaneously. For instance, with 90 fruits on Tuesday, the weekly total becomes 522 and the weekly average becomes 522 / 7 which is not exactly 75. Only 93 satisfies both average conditions together.

Common Pitfalls:
Some students mistakenly divide the difference of the averages by the number of days or miscount the number of days in the week. Others attempt to average the two given averages directly. The correct method is always to convert each average to a total using the corresponding number of days, then subtract to isolate the unknown day total.

Final Answer:
The number of fruits offered on Tuesday is 93.