Exams › SSC CGL (Prelims) › General › Time and Distance
12 questions with worked solutions.
Q1. A train covers 1.2 km in 1 minute. How far will it travel in 2 hours 15 minutes?
Answer: 162 km
The train covers 1.2 km per minute. In 2 hours 15 minutes, the time is 135 minutes. So the distance covered is $1.2 \times 135 = 162$ km.
Answer: 1344 km/h
Distance covered in 4 hours = 280 × 4 = 1120 km. To cover 1120 km in 50 minutes = 5/6 hour, required speed = 1120 ÷ (5/6) = 1344 km/h.
Answer: 300 km
Let distance be d and scheduled time be t. Then d/60 = t - 1.5 and d/40 = t + 1. Subtracting gives d/40 - d/60 = 2.5, so d/120 = 2.5 and d = 300 km.
Answer: 60 km
The slower cyclist's speed is 18 km/h, so the faster cyclist's speed is \(18\times\frac{4}{3}=24\) km/h. Relative speed is \(24-18=6\) km/h, so time to catch up is \(15/6=2.5\) hours. In that time, the faster cyclist travels \(24\times2.5=60\) km.
Q5. Rohit covers half of his journey at 15 km/h and the remaining half at 10 km/h. His average speed is:
Answer: 12 km/h
When equal distances are covered at two different speeds, average speed is \(\frac{2ab}{a+b}\). Substituting \(a=15\) and \(b=10\) gives \(\frac{2\cdot15\cdot10}{15+10}=12\) km/h.
Answer: 6 km
When two people move in the same direction, their separation increases at the relative speed, which is the difference of their speeds. Here, the relative speed is 8 - 6 = 2 km/h, so in 3 hours the distance between them becomes 2 × 3 = 6 km.
Answer: 24 km
Let the distance be \(d\) km. Then the extra time is \(\frac{d}{18}-\frac{d}{20}=\frac{8}{60}\) hours. Solving gives \(d=24\) km.
Answer: 510 km
The train travels from 6:00 a.m. to 2:30 p.m., which is 8.5 hours. Distance = speed × time = $60 \times 8.5 = 510$ km.
Q9. A train covers 216 km in 3 hours. What is its average speed in metres per second?
Answer: 20 m/sec
The train’s speed is 216 ÷ 3 = 72 km/h. Converting to m/s: 72 × 5/18 = 20 m/s.
Q10. A person crosses a 700 m long street in 5 minutes. What is his speed in km/h?
Answer: 8.4 km/h
Speed = distance/time = 700 m / 5 min = 140 m/min. Converting to km/h: $140\times \frac{60}{1000} = 8.4$ km/h. So the correct speed is 8.4 km/h.
Answer: 64 km/h
When they move towards each other, the sum of speeds is 480/5 = 96 km/h. When they move in the same direction, the difference of speeds is 480/15 = 32 km/h. Solving M + N = 96 and M - N = 32 gives M = 64 km/h.
Q12. A train travels 1.2 km every minute. What distance will it cover in 2 hours and 15 minutes?
Answer: 162 km
The train covers 1.2 km in 1 minute. In 2 hours 15 minutes, the time is 135 minutes. So the distance covered is 1.2 × 135 = 162 km.