Worked Solution
✓ VerifiedStatement Showing Cost per Tonne Kilometre of Carrying Coal from Mine X and Mine Y
Lorry Carrying Capacity: 4 tonnes | Average Speed: 40 km/hr
Time per Trip:
For Mine X (distance = 15 km, round trip = 30 km):
- Travel time (round trip): 30 km ÷ 40 km/hr = 0.75 hrs = 45 minutes
- Loading time at Mine X: 30 minutes
- Unloading time at rail head: 15 minutes
- Total time per trip = 90 minutes = 1.5 hours
For Mine Y (distance = 20 km, round trip = 40 km):
- Travel time (round trip): 40 km ÷ 40 km/hr = 1 hr = 60 minutes
- Loading time at Mine Y: 25 minutes
- Unloading time at rail head: 15 minutes
- Total time per trip = 100 minutes = 5/3 hours
Cost per Trip:
| Particulars | Mine X | Mine Y |
|---|---|---|
| Time-based costs (Drivers' wages, depreciation, insurance, taxes @ ₹12/hr) | 1.5 × ₹12 = ₹18.00 | 5/3 × ₹12 = ₹20.00 |
| Distance-based costs (Fuel, oil, tyres, repairs @ ₹1.60/km) | 30 km × ₹1.60 = ₹48.00 | 40 km × ₹1.60 = ₹64.00 |
| Total Cost per Trip | ₹66.00 | ₹84.00 |
Tonne-Kilometres per Trip:
- Mine X: 4 tonnes × 15 km = 60 tonne-km
- Mine Y: 4 tonnes × 20 km = 80 tonne-km
Cost per Tonne-Kilometre:
- Mine X: ₹66 ÷ 60 = ₹1.10 per tonne-km
- Mine Y: ₹84 ÷ 80 = ₹1.05 per tonne-km
Conclusion: Despite Mine Y being farther, its cost per tonne-km (₹1.05) is lower than Mine X (₹1.10), primarily because Mine Y has a shorter loading time (25 min vs 30 min), making it marginally more cost-efficient on a tonne-km basis.
Write it like this
1The skeleton
- Head your answer with a bold statement title — write 'Statement Showing Cost per Tonne-Kilometre' on line one so the examiner's eye lands on it instantly; headings signal you know this is a formal costing statement, not a rough working.
- Calculate total time per trip FIRST before touching any costs — time = travel (round trip ÷ speed) + loading + unloading; examiners award a step mark here, so isolate it visually with sub-bullets for each mine.
- Split costs into two explicit rows: time-based and distance-based — ₹12/hr is time-driven, ₹1.60/km is distance-driven; presenting them in separate rows shows you understand cost behaviour and earns the classification mark most students skip.
- Calculate tonne-km as a separate labelled step — write '4 tonnes × 15 km = 60 tonne-km' explicitly; do NOT bury this inside the final division, because examiners tick it as a distinct computation.
- Present both mines in a single comparative table — side-by-side columns let the examiner verify both mines in one scan and signals exam-ready format; a narrative paragraph for each mine loses time and clarity marks.
- End with a one-line conclusion comparing the two costs — state which mine is cheaper per tonne-km and the reason (loading time difference); ICAI model answers always close transport questions with a brief inference, and that last line often carries 1 mark.
2Examiner-rewarded phrases
3Common trap
Heads up — the single biggest killer here is using one-way distance (15 km / 20 km) for fuel cost instead of round-trip (30 km / 40 km). The lorry has to come BACK empty, so distance-based costs double; your time calculation already uses round trip implicitly via speed, so if your fuel cost doesn't match, the examiner knows you missed it.