A factory buys 7 machines: two of type A at Rs. 95,000 each, two of type B at Rs. 75,000 each, and the remaining machines of type C at Rs. 43,000 each. What is the average cost (in rupees) of these seven machines?

Introduction / Context:
This problem requires computing the average cost of several machines bought at different prices. We know how many machines of each type were bought and their individual costs. From this we can obtain the total cost and then divide by the total number of machines to find the average cost per machine.

Given Data / Assumptions:

• Number of machines of type A = 2, each costing Rs. 95,000.
• Number of machines of type B = 2, each costing Rs. 75,000.
• Total number of machines = 7, so machines of type C = 7 - 4 = 3.
• Each machine of type C costs Rs. 43,000.

Concept / Approach:
The average cost is defined as: Average cost per machine = total cost of all machines / total number of machines. So we first calculate the total cost contributed by each machine type, add them to get the grand total, and then divide by 7.

Step-by-Step Solution:
Step 1: Compute total cost of type A machines. Total cost of type A = 2 * 95,000 = Rs. 190,000. Step 2: Compute total cost of type B machines. Total cost of type B = 2 * 75,000 = Rs. 150,000. Step 3: Compute total cost of type C machines. Number of type C machines = 3. Total cost of type C = 3 * 43,000 = Rs. 129,000. Step 4: Compute grand total cost. Grand total = 190,000 + 150,000 + 129,000 = Rs. 469,000. Step 5: Compute average cost per machine. Average cost = 469,000 / 7 = Rs. 67,000.

Verification / Alternative check:
We can check the division: 67,000 * 7 = 469,000, which matches the total cost computed from individual machines. Also, the average cost lies between the highest price (Rs. 95,000) and the lowest price (Rs. 43,000), which is logically necessary, so the answer is reasonable.

Why Other Options Are Wrong:
An average of Rs. 71,000 would give a total of 7 * 71,000 = Rs. 497,000, which is higher than the actual total cost. An average of Rs. 75,000 gives an even higher total and is impossible given three machines cost only Rs. 43,000 each. An average of Rs. 65,500 gives a total of 458,500 rupees, which is too low. Only Rs. 67,000 reproduces the correct total of Rs. 469,000.

Common Pitfalls:
Some students mistakenly average the three price tags directly, ignoring the fact that there are different numbers of each machine type. Others may miscount the number of machines of type C or make arithmetic errors when adding large numbers. Always multiply each unit cost by its quantity, sum these totals, and divide by the total number of units to find the correct weighted average.

Final Answer:
The average cost of the seven machines is Rs. 67,000 per machine.