The average number of fruits offered in a temple over a full week of seven days is 75. The average for six days excluding Tuesday is 72. How many fruits were offered on Tuesday?

Introduction / Context:
This is a classic average problem where we know the average number of items over a full period and also the average over a subset of that period. Using these two averages, we can find the value for the missing day, which in this case is Tuesday. Such questions train you to manipulate totals and averages quickly.

Given Data / Assumptions:

• Number of days in the week considered = 7.
• Average fruits offered over all 7 days = 75.
• Average fruits offered over 6 days excluding Tuesday = 72.
• We need to find the number of fruits offered on Tuesday.

Concept / Approach:
The basic relation is: Total fruits over a period = average fruits * number of days. Using this, we will compute:

• Total fruits over 7 days.
• Total fruits over the 6 days excluding Tuesday.

Then Tuesday fruits = total for 7 days minus total for the other 6 days.

Step-by-Step Solution:
Step 1: Compute the total number of fruits offered over 7 days. Total over 7 days = 75 * 7 = 525 fruits. Step 2: Compute the total number of fruits offered on the 6 days excluding Tuesday. Total over 6 days = 72 * 6 = 432 fruits. Step 3: Compute fruits offered on Tuesday. Tuesday fruits = total 7 day fruits - total 6 day fruits. Tuesday fruits = 525 - 432 = 93 fruits.

Verification / Alternative check:
We can verify by recomputing the overall average including Tuesday. If the six days have a total of 432 fruits and Tuesday has 93 fruits, then total for 7 days is 432 + 93 = 525. The average is 525 / 7 = 75 fruits per day, which matches the given weekly average, so the value is consistent.

Why Other Options Are Wrong:
If Tuesday had 90 fruits, the total for the week would be 432 + 90 = 522 and the average 522 / 7 = 74.57, not 75. If Tuesday had 72 fruits, the weekly average would be too low. If Tuesday had 92 fruits, the weekly average would be 524 / 7, again not 75. Only 93 fruits gives the correct weekly average of 75.

Common Pitfalls:
A common mistake is to average the two averages directly, or to assume Tuesday also had 72 or 75 fruits. Another pitfall is forgetting to multiply the averages by the number of days to get totals. Always work with totals when combining or separating averages across different numbers of items or days.

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