The average cost of 5 items in a shopping list is Rs 650. If one more item costing Rs 1400 is added to the list, what will be the new average cost (in rupees) of all the 6 items together?

Introduction / Context:
This question uses a simple average and total-cost relationship. We are given the average cost of 5 items and then introduce a sixth, more expensive item to the list. The task is to calculate the new average cost of all 6 items combined.

Given Data / Assumptions:

• Average cost of first 5 items = Rs 650.
• Cost of each of those 5 items can be different, but only the average is known.
• Cost of the 6th item = Rs 1400.
• We must find the new average cost of all 6 items.

Concept / Approach:
We use the formula: average = total cost / number of items. First find the total cost of the original 5 items from the given average. Then add the cost of the sixth item to get the total cost of 6 items. Finally, divide by 6 to get the new average. No individual item cost needs to be known exactly beyond this.

Step-by-Step Solution:
Step 1: Compute total cost of the first 5 items. Total(5 items) = 5 * 650 = Rs 3250. Step 2: Add the 6th item costing Rs 1400. Total(6 items) = 3250 + 1400 = Rs 4650. Step 3: Compute new average cost. New average = 4650 / 6. Step 4: Divide carefully: 6 * 700 = 4200, remainder 450. 6 * 75 = 450, so 4200 + 450 = 4650. Therefore, 4650 / 6 = 775.
Verification / Alternative check:
We can confirm: 6 * 775 = 4650, which matches the computed total cost, so the new average is consistent.
Why Other Options Are Wrong:
An average of 875 or 825 or 725 or 700 would give total costs that do not match the known total of Rs 4650. For example, if the new average were 825, total = 6 * 825 = 4950, which is too high.
Common Pitfalls:
Sometimes students mistakenly average 650 and 1400 directly, ignoring the fact that the average of 5 items and a single item must be weighted by 5 and 1, respectively. Another error is miscalculating the total for 5 items by adding 650 five times incorrectly rather than multiplying efficiently.
Final Answer:
The new average cost of all 6 items is Rs 775.