Question

Fixed cost per year and variable cost per hour of a tractor were estimated based on its annual usage of 800 h. The total cost of operation was found to be Rs. 540 per hour. It was later re-estimated and found that the total cost of operation would be Rs. 510 per hour, if the annual hours of use were increased to 1000 h. Considering all the components of annual usage cost to be the same, the variable cost in Rs. per hour would be \(\underline{\hspace{1cm}}\) (answer in integer).

Hint:

When increasing hours of usage, the variable cost is solved by setting up the total cost equations for both scenarios.

Answer 1

Correct Answer: 385

Let the fixed cost per year = \(F\) and the variable cost per hour = \(V\).
For 800 hours: \[ \text{Total cost} = F + 800V = 540 \times 800 = 432000 \] For 1000 hours: \[ \text{Total cost} = F + 1000V = 510 \times 1000 = 510000 \] Subtracting the first equation from the second: \[ (F + 1000V) - (F + 800V) = 510000 - 432000 \] \[ 200V = 78000 \] \[ V = \frac{78000}{200} = 390 \] Thus, the variable cost is \( \boxed{390} \ \text{Rs per hour} \).