The average cost of 4 items in a shopping list is Rs 1250. If one more item costing Rs 2000 is added to the list, what will be the new average cost in rupees?

Introduction / Context:
This problem involves updating an average when an additional value is added to the data set. You know the average cost of 4 items and the cost of a 5th item that is added. The task is to find the new average cost of all 5 items.

Given Data / Assumptions:

• Number of items initially = 4.
• Average cost of these 4 items = Rs 1250.
• Cost of the additional 5th item = Rs 2000.
• We need the new average cost of all 5 items in rupees.

Concept / Approach:
When a new item is added, the total cost changes. First we compute the total cost of the initial 4 items using their average. Then we add the cost of the new item to get the new total cost. Finally, we divide the new total by 5 to get the updated average. Since the new item is more expensive than the initial average, the overall average will increase.

Step-by-Step Solution:
Step 1: Total cost of the first 4 items = 4 * 1250 = Rs 5000. Step 2: Cost of the new 5th item = Rs 2000. Step 3: New total cost for all 5 items = 5000 + 2000 = Rs 7000. Step 4: New number of items = 5. Step 5: New average cost = 7000 / 5 = Rs 1400.

Verification / Alternative check:
We can see that the additional item costs Rs 750 more than the old average of Rs 1250. When this extra 750 is spread over 5 items, the average increases by 750 / 5 = Rs 150. Adding this to 1250 gives 1400, which agrees with our direct calculation. This confirms that the new average is correct.

Why Other Options Are Wrong:
Option 1100 is less than the original average and cannot be correct because we have added a more expensive item. Option 1500 would correspond to total cost 7500, which is higher than the actual total 7000. Option 1250 is the old average before adding the item and does not reflect the new data. Only 1400 matches the correct total and the direction of change.

Common Pitfalls:
Some learners mistakenly average 1250 and 2000 directly, which assumes both parts have the same count of items. Others forget to change the denominator from 4 to 5 after adding the new item. Always update both the total and the number of items whenever a new value is added to a data set.

Final Answer:
The new average cost of the items is Rs 1400.