Mahesh buys 3 shirts at an average price of Rs 1250 per shirt. He then buys 2 more shirts at an average price of Rs 1450 per shirt. What is the average price (in Rs) of all 5 shirts taken together?

Introduction / Context:
This question is about combining two groups with different averages to find a combined average. Mahesh buys some shirts at one average price and then buys more shirts at a different average price. You must determine the overall average price per shirt for all of his purchases.

Given Data / Assumptions:
• Number of shirts in the first purchase = 3.• Average price in the first purchase = Rs 1250 per shirt.• Number of shirts in the second purchase = 2.• Average price in the second purchase = Rs 1450 per shirt.• All prices are in rupees.

Concept / Approach:
The combined average is found by calculating the total cost of all shirts and dividing by the total number of shirts. We first convert each group's average into a total cost, then sum these totals, and finally divide by the total quantity to get the required average.

Step-by-Step Solution:
Step 1: Total cost of the first 3 shirts = 3 * 1250 = Rs 3750.Step 2: Total cost of the next 2 shirts = 2 * 1450 = Rs 2900.Step 3: Total cost of all 5 shirts = 3750 + 2900 = Rs 6650.Step 4: Total number of shirts = 3 + 2 = 5.Step 5: Combined average price = total cost / total number of shirts = 6650 / 5.Step 6: 6650 / 5 = Rs 1330.

Verification / Alternative check:
Note that the second group of shirts is more expensive than the first, so the combined average must be between 1250 and 1450, but closer to 1250 because there are more shirts from the cheaper batch. The calculated value of 1330 lies in this reasonable range and therefore makes sense.

Why Other Options Are Wrong:
1370, 1390: These are too high given that only 2 out of 5 shirts are from the more expensive batch.1310: This is lower than the balanced value determined from the exact ratio of cheaper and costlier shirts.

Common Pitfalls:
Students may incorrectly average the two given averages directly without weighting by quantity, for example taking (1250 + 1450) / 2. This approach ignores that the number of shirts in each group is different. Always convert to totals first and then divide by the total quantity.

Final Answer:
The average price of all 5 shirts is Rs 1330.