Question

The table shows the data of running a machine for five years. The original machine cost is Rupees 70,000. In order to minimize the average total cost per year for running the machine, the machine should be replaced after ............. years. (Answer in integer) 

Hint:

To minimize the average total cost per year, compare the average costs for each year and select the year with the lowest value.

Answer 1

Correct Answer: 4

 To determine the optimal number of years to run the machine before replacing it, we aim to minimize the average total cost per year. The total cost includes the original cost minus resale value plus maintenance costs.

Step-by-step Calculation:

Year	Total Cost (Rupees)	Average Total Cost Per Year (Rupees)
1	70000 - 40000 + 19100 = 49100	49100 / 1 = 49100
2	70000 - 30000 + 19100 + 20300 = 79400	79400 / 2 = 39700
3	70000 - 25000 + 19100 + 20300 + 23500 = 107900	107900 / 3 ≈ 35967
4	70000 - 22000 + 19100 + 20300 + 23500 + 30500 = 139400	139400 / 4 = 34850
5	70000 - 20000 + 19100 + 20300 + 23500 + 30500 + 40000 = 179400	179400 / 5 = 35880

The average total cost per year is minimized at 34850 Rupees for 4 years.

Therefore, the machine should be replaced after 4 years which fits the given range (4, 4).