What is the time required to grade and finish 30 km of road formation with width equal to thrice the width of the motor grader, using six passes of the motor grader with speed for each of the successive two passes as 6 km/h, 8 km/h and 10 km/h, respectively ? (Take machine efficiency based on operator’s skill, machine characteristics and working conditions as 75%)
- A45 hours
- B15 hours
- C90 hoursCorrect
- D60 hours
Solution
Concept
Time for grading with multiple passes
Formula
T = Σ (passes × D / S) × (number of strips) / E
Step-by-step solution
1. For one strip: (2 × 30/6 + 2 × 30/8 + 2 × 30/10) = 10 + 7.5 + 6 = 23.5 h. 2. Width = 3 × blade width, so 3 strips: 3 × 23.5 = 70.5 h. 3. With 75% efficiency: 70.5 / 0.75 = 94 h ≈ 90 hours.
Explanation
The time is the total travel distance divided by the speed of each pass, multiplied by the number of strips and divided by the efficiency.
Why the other options are wrong
15, 45 and 60 hours are well below the 94 hours obtained. 90 hours is the closest option.
Shortcut
Σ D·n/S × strips ÷ efficiency.
Common mistake
Ignoring the three-strip width factor (gives 31 h).
Correct answer: C) 90 hours