The average cost of 4 items in a shopping list is Rs 1,250 per item. If one more item costing Rs 2,000 is added to the list, what will be the new average cost (in Rs) per item for all 5 items together?

Introduction / Context:
This question deals with updating an average when a new item is added to an existing group. It helps to understand how the inclusion of a more expensive or cheaper item affects the overall average cost of all items combined.

Given Data / Assumptions:
• Number of items initially = 4.• Average cost of these 4 items = Rs 1,250.• Cost of the new 5th item = Rs 2,000.• All costs are in rupees.

Concept / Approach:
To update an average when a new value is added, we first compute the total cost of the original items using the initial average. Then we add the cost of the new item to get the new total and divide by the new number of items to get the new average. Since the new item is more expensive than the original average, we expect the overall average to increase.

Step-by-Step Solution:
Step 1: Let the total cost of the initial 4 items be S.Step 2: Since the average cost is 1,250, S = 4 * 1,250.Step 3: Compute S = 5,000.Step 4: Add the cost of the 5th item, which is Rs 2,000.Step 5: New total cost = 5,000 + 2,000 = 7,000.Step 6: New number of items = 5.Step 7: New average cost = new total cost / number of items = 7,000 / 5.Step 8: 7,000 / 5 = 1,400.

Verification / Alternative check:
The new item costs Rs 750 more than the original average (2,000 minus 1,250). When you spread this extra 750 over 5 items, the average should increase by 750 / 5 = 150. So the new average should be 1,250 + 150 = 1,400, which matches our detailed calculation.

Why Other Options Are Wrong:
1100: This is lower than the original average and cannot happen when a more expensive item is added.1500: This overestimates the impact of the costlier item.1250: This is the original average, before adding the more expensive fifth item.

Common Pitfalls:
Some students forget to multiply the original average by the number of items to find the total, or they mistakenly average the old average and the new value directly without considering the differing counts. Always convert averages into totals before combining or updating groups.

Final Answer:
The new average cost per item is Rs 1,400.