A factory buys 10 machines in total: 2 of type A, 3 of type B and the remaining 5 of type C. The prices of machines A, B and C are Rs 95,000, Rs 60,000 and Rs 50,000 respectively. What is the average cost (in rupees) of all these machines together?

Introduction / Context:
This question focuses on finding the average cost of a group of items when different quantities of each type are purchased at different prices. It is a weighted average problem, where we multiply each price by the number of items of that type, add these products, and then divide by the total number of items.

Given Data / Assumptions:

• Total number of machines = 10.
• Number of type A machines = 2, price per machine = Rs 95,000.
• Number of type B machines = 3, price per machine = Rs 60,000.
• Remaining machines are type C, so number of type C machines = 10 - 2 - 3 = 5, price per machine = Rs 50,000.
• Required: average cost of all 10 machines.

Concept / Approach:
Average cost is computed as total cost divided by total number of machines. Since each type has a different cost and count, we compute the total cost by summing individual costs: (number of A * price of A) + (number of B * price of B) + (number of C * price of C). Then we divide this total by 10 to obtain the average cost per machine.

Step-by-Step Solution:
Total cost of type A machines = 2 * 95000 = Rs 190000. Total cost of type B machines = 3 * 60000 = Rs 180000. Total cost of type C machines = 5 * 50000 = Rs 250000. Total cost of all machines = 190000 + 180000 + 250000. Total cost = Rs 620000. Total number of machines = 10. Average cost per machine = total cost / total number. Average cost = 620000 / 10 = Rs 62000.
Verification / Alternative check:
Compute approximate average by observation: prices range from Rs 50000 to Rs 95000. Most machines (3 + 5 = 8 machines) cost Rs 60000 or Rs 50000, while only 2 machines cost Rs 95000. So the overall average must be somewhat above Rs 55000 but clearly less than Rs 70000. The value Rs 62000 fits well in this reasonable range, supporting our detailed calculation.
Why Other Options Are Wrong:
Option B (68333): Too high given that only 2 machines are costly; it overestimates total cost. Option C (74666): Even higher and impossible given the mixture of cheaper machines. Option D (60500): Closer but still not equal to the exact computed average of 62000. Option A (62000): Matches the correct calculation of total cost divided by number of machines.
Common Pitfalls:
Some students try to simply average the three prices without considering the different quantities of each type. Others may miscount the number of type C machines by not subtracting correctly. Calculation slips in multiplying or adding large numbers may also lead to incorrect answers.
Final Answer:
The average cost of all 10 machines is Rs 62000.