Mahesh buys 3 shirts at an average price of Rs 1250 each. He then buys 2 more shirts at an average price of Rs 1450 each. What is the overall average price in rupees of all 5 shirts that he buys?

Introduction / Context:
This question is a direct application of the concept of weighted average. Mahesh buys two sets of shirts at different average prices and we must determine the combined average price for all the shirts together. Such questions appear frequently in aptitude tests and are useful for understanding how averages combine across groups with different sizes and values.

Given Data / Assumptions:
- First purchase: 3 shirts at an average price of Rs 1250 each.
- Second purchase: 2 shirts at an average price of Rs 1450 each.
- Total number of shirts purchased altogether = 5.
- We must find the overall average price per shirt for all 5 shirts.

Concept / Approach:
The overall average price is calculated by dividing the total amount spent by the total number of shirts. We first compute the cost of the first group and the cost of the second group. Then we add these costs to get the total expenditure and divide by the total number of shirts. This is an example of combining averages using weighted sums rather than simply averaging the two averages directly.

Step-by-Step Solution:
Step 1: Cost of the first 3 shirts = 3 * 1250 = Rs 3750.Step 2: Cost of the next 2 shirts = 2 * 1450 = Rs 2900.Step 3: Total cost for all 5 shirts = 3750 + 2900 = Rs 6650.Step 4: Total number of shirts = 3 + 2 = 5.Step 5: Overall average price per shirt = total cost / total number of shirts = 6650 / 5.Step 6: Compute 6650 / 5 = 1330.Step 7: Therefore, the average price of all 5 shirts is Rs 1330.

Verification / Alternative check:
The two group averages are 1250 and 1450. Since Mahesh bought slightly fewer shirts at the higher price (2 shirts) compared to the cheaper ones (3 shirts), the combined average should be closer to 1250 than to 1450, but still greater than 1250. The value 1330 fits this expectation, confirming that the result is reasonable as well as mathematically correct.

Why Other Options Are Wrong:
An average of 1370 or 1390 would place the combined average too close to or above the higher segment average of 1450, which is not possible when more shirts were bought at the lower price. Averages of 1310 or 1290 are lower than the true combined average 1330 and do not match the correct total expenditure when multiplied by 5.

Common Pitfalls:
Many students mistakenly take the average of 1250 and 1450 directly, that is (1250 + 1450) / 2 = 1350, ignoring the fact that the number of shirts in each price group is different. To avoid this, always compute the total expenditure for each group and then find the overall average from the grand total and total quantity.

Final Answer:
The overall average price of the 5 shirts is Rs 1330 per shirt.