The average cost of 5 items in a shopping list is Rs 650. If another item costing Rs 1400 is added to the list, what will be the new average cost in rupees?

Introduction / Context:
This is a straightforward question on averages where an additional value is added to an existing data set. It illustrates how the mean changes when a new item with a different cost is introduced.

Given Data / Assumptions:
- The original number of items is 5.
- The average cost of these 5 items is Rs 650.
- A sixth item costing Rs 1400 is added.
- We need the new average cost of all 6 items.

Concept / Approach:
The average is equal to total sum divided by the number of items. So we first find the total cost of the original 5 items from their average. Then we add the cost of the sixth item to get the new total and finally divide by 6 to get the new average.

Step-by-Step Solution:
Step 1: Total cost of 5 items = average cost * number of items = 650 * 5. Step 2: Compute 650 * 5 = 3250 rupees. Step 3: Add the cost of the sixth item: new total = 3250 + 1400 = 4650 rupees. Step 4: The number of items is now 6, so the new average cost = 4650 / 6. Step 5: Compute 4650 / 6 = 775.

Verification / Alternative check:
Check by approximate reasoning: the new item is more expensive than the old average, so the new average must be higher than 650. The value 775 is higher than 650 but not extremely large, which fits the data well. Calculations also confirm this exactly.

Why Other Options Are Wrong:
- Option 875: This would imply a total of 875 * 6 = 5250, which is greater than 4650, so it is impossible.

- Option 725: This corresponds to a total of 4350, which is less than the true total 4650 and therefore too small.

- Option 825: This would imply a total of 4950, which again does not match the correct total.

Common Pitfalls:
A common mistake is to simply average 650 and 1400, which would ignore the fact that there are already 5 items at 650. Always return to the fundamental definition of average: total sum divided by count. From there, all such questions can be solved reliably.

Final Answer:
The new average cost of the items is 775 rupees.