A factory buys 7 machines in total: 2 machines of type A, 4 machines of type B and the remaining 1 machine of type C. The prices of machines A, B and C are Rs 56,000, Rs 45,000 and Rs 30,000 respectively. What is the average cost (in rupees) of these 7 machines?

Introduction / Context:
This is another weighted average cost question. The factory buys machines of three different types at different prices and in different quantities. We need to compute the total cost and then find the average cost per machine.

Given Data / Assumptions:

• Total machines purchased = 7.
• Type A: 2 machines, each costing Rs 56,000.
• Type B: 4 machines, each costing Rs 45,000.
• Type C: 1 machine, costing Rs 30,000.
• We have to find the average cost of these 7 machines.

Concept / Approach:
Average cost is defined as total cost divided by total number of items. Since there are different quantities and prices for machine types, we compute the total cost for each type by multiplying the quantity by the unit price and then sum them up. Dividing this total by 7 gives the average cost per machine.

Step-by-Step Solution:
Total cost of type A machines = 2 * 56000 = Rs 112000. Total cost of type B machines = 4 * 45000 = Rs 180000. Total cost of type C machines = 1 * 30000 = Rs 30000. Total cost of all machines = 112000 + 180000 + 30000. Total cost = Rs 322000. Total number of machines = 7. Average cost per machine = total cost / number of machines. Average cost = 322000 / 7 = Rs 46000.
Verification / Alternative check:
We can approximate: most machines are in the mid range (Rs 45000) and a few are slightly more expensive (Rs 56000) or cheaper (Rs 30000). So the average should be around the middle of this price range, and 46000 fits this expectation very well.
Why Other Options Are Wrong:
Option B (43666.66): Lower than the correct average and does not match the exact total cost when multiplied by 7. Option C (41333.33): Even lower and clearly underestimates the influence of the more expensive machines. Option D (44500): Close but still not equal to the correct exact average of 46000. Option A (46000): Exactly matches the calculated average, so it is correct.
Common Pitfalls:
Some students average the three prices directly without considering that there are different numbers of each machine type. Others may mistakenly think that the average of 56000 and 45000 must be taken first and then adjusted incorrectly. Arithmetic errors in multiplying or adding the costs may also lead to a wrong average.
Final Answer:
The average cost of the 7 machines is Rs 46000.