Rita buys 5 sarees at an average cost of Rs 2250 each. She then buys 3 more sarees at an average cost of Rs 2750 each. What is the overall average cost (in rupees) of all 8 sarees that she buys?

Introduction / Context:
This question involves combining two groups with different averages to find a new overall average. Rita buys sarees in two batches at different average prices. We need to compute the total cost from these averages and then determine the combined average. This is a straightforward weighted average problem.

Given Data / Assumptions:

• First batch: 5 sarees, average cost = Rs 2250 each.
• Second batch: 3 sarees, average cost = Rs 2750 each.
• Total sarees purchased = 5 + 3 = 8.
• We need the overall average cost per saree.

Concept / Approach:
Average cost is defined as total cost divided by total number of items. When averages for subgroups are known, we can recover the total cost of each group by multiplying the group average by the group size. Then we sum these totals and divide by the total number of sarees to get the combined average.

Step-by-Step Solution:
First batch: number of sarees = 5, average cost = Rs 2250. Total cost of first batch = 5 * 2250 = Rs 11250. Second batch: number of sarees = 3, average cost = Rs 2750. Total cost of second batch = 3 * 2750 = Rs 8250. Total number of sarees = 5 + 3 = 8. Total cost of all sarees = 11250 + 8250 = Rs 19500. Overall average cost = total cost / total number. Overall average = 19500 / 8 = Rs 2437.5.
Verification / Alternative check:
We can approximate: since most sarees are bought at Rs 2250 and some at Rs 2750, the final average should lie between these two values. 2437.5 is indeed between 2250 and 2750, and closer to 2250, which is reasonable because more sarees were bought at the lower price.
Why Other Options Are Wrong:
Option B (2500): Slightly higher than the correct average, ignoring the fact that more sarees were bought at the cheaper price. Option C (2450): Close but does not match the exact calculation. Option D (2332.5): Too low and does not reflect the effect of higher cost sarees. Option A (2437.5): Matches the exact computed overall average, so it is correct.
Common Pitfalls:
A common error is to simply take the average of 2250 and 2750 without considering how many sarees were bought in each batch. Some students mistakenly divide the sum of the two averages by 2, which ignores the different group sizes. Calculation mistakes when multiplying or adding large numbers can also cause wrong answers.
Final Answer:
The overall average cost of all 8 sarees is Rs 2437.5.