A factory buys 10 machines: 1 machine of type A, 4 machines of type B and the remaining machines of type C. Their prices are Rs 90000 for type A, Rs 40000 for each type B and Rs 40000 for each type C. What is the average cost of these 10 machines (in rupees)?

Introduction / Context:
This is a straightforward average cost question involving different categories of machines purchased at given prices. By calculating the total cost of all machines and dividing by the number of machines, we obtain the average cost per machine. Problems like this appear in profit and loss or basic arithmetic sections to check whether candidates can systematically handle grouped data.

Given Data / Assumptions:
- Total number of machines = 10
- Number of type A machines = 1, price per machine = Rs 90000
- Number of type B machines = 4, price per machine = Rs 40000
- Remaining machines are type C, so number of type C machines = 10 − 1 − 4 = 5
- Price per type C machine = Rs 40000
- We assume all prices are in rupees and there are no extra costs such as tax or transport charges.

Concept / Approach:
The average cost per machine is given by total cost of all machines divided by total number of machines. We therefore find the cost contribution from each type separately: type A contributes one expensive machine, types B and C contribute several machines at a lower but equal price. Then we sum these contributions and divide by 10 to get the required average.

Step-by-Step Solution:
Step 1: Cost of type A machines = 1 × 90000 = Rs 90000.Step 2: Cost of type B machines = 4 × 40000 = Rs 160000.Step 3: Cost of type C machines = 5 × 40000 = Rs 200000.Step 4: Total cost of all machines = 90000 + 160000 + 200000 = Rs 450000.Step 5: Average cost per machine = total cost ÷ number of machines = 450000 ÷ 10 = Rs 45000.

Verification / Alternative check:
We can check by inspection that most machines (9 out of 10) cost Rs 40000, and one machine costs Rs 90000, which is Rs 50000 more than 40000. When this extra Rs 50000 is spread over 10 machines, each machine effectively carries an extra Rs 5000 over 40000. Therefore average cost = 40000 + 5000 = Rs 45000, which agrees with the detailed calculation above.

Why Other Options Are Wrong:
An average like 56666.6 or 68333.3 is far too high, since only one machine is more expensive than Rs 40000 and the remaining nine machines are at 40000. Similarly, values like 43500 or 40000 underestimate the effect of the single Rs 90000 machine. Only Rs 45000 correctly reflects the influence of one high cost machine among nine lower cost machines.

Common Pitfalls:
Students sometimes average the three prices 90000 and 40000 and 40000 directly without weighting them by the number of machines, which is incorrect because different types occur in different quantities. Others may forget to count how many machines are of type C and instead assume an incorrect split. Always ensure that each price is multiplied by its correct quantity when calculating total cost.

Final Answer:
The average cost of the 10 machines is 45000 rupees per machine.