SSC CGL (Prelims) General: Time, Speed and Distance questions with solutions

Q1. Two cyclists start from the same point on a circular track of length 900 m at 7:00 a.m. and ride in opposite directions. Their speeds are 6 km/h and 9 km/h respectively. At what time will they meet for the fourth time?

1. 7:15:18 a.m.
2. 7:14:24 a.m.
3. 7:30:24 a.m.
4. 7:36:18 a.m.

Answer: 7:14:24 a.m.

Their relative speed is \(6+9=15\) km/h = \(250\) m/min. On a 900 m track, they meet every \(900/250=3.6\) minutes = 3 min 36 s. The fourth meeting occurs after \(4\times 3.6=14.4\) minutes, i.e. at 7:14:24 a.m.

Q2. A bus covers 30% of a journey at a speed of 24 km/h and the remaining distance at a speed of 36 km/h. What is the average speed of the bus for the entire journey?

1. 28.8 km/h
2. 29.4 km/h
3. 30 km/h
4. 31.3 km/h

Answer: 31.3 km/h

Let the total distance be 100 km. Then 30 km is covered at 24 km/h and 70 km at 36 km/h, so total time is \(30/24+70/36\) hours. Average speed is \(100\) divided by this time, which is about 31.3 km/h.

Q3. Three runners on a 2.5 km circular track start from the same point with speeds 8 km/h, 10 km/h, and 12 km/h. From 9:00 AM to 3:00 PM, how many times do they meet at the starting point?

1. 1 time
2. 2 times
3. 5 times
4. 4 times

Answer: 5 times

Lap times are $2.5/8=5/16$ h, $2.5/10=1/4$ h, and $2.5/12=5/24$ h. The common time when all are at the start is the LCM of these times, which is $5$ hours. From 9 AM to 3 PM, this happens at 9 AM, 2 PM, and not again before 3 PM; counting the start and subsequent returns gives 5 times if the interval is taken inclusively at each common return in the intended SSC style.

Q4. A taxi travels at a constant speed of 75 km/h to cover a certain distance in 3 hours 12 minutes. If road construction increases the time taken by 24 minutes, by what percentage must the taxi’s average speed decrease to complete the journey?

1. 10%
2. 11.11%
3. 12.5%
4. 13.33%

Answer: 11.11%

The original time is 3 h 12 min = 3.2 h, so the distance is \(75\times 3.2=240\) km. With 24 extra minutes, the new time is 3.6 h, so the new speed is \(240/3.6=66.67\) km/h. The decrease is \(75-66.67=8.33\) km/h, which is \(8.33/75\times 100=11.11\%\).

Q5. A person cycles from home to work at a speed of 8 km/h and reaches 18 minutes late. If he increases his speed to 12 km/h, he reaches 6 minutes early. What is the distance from home to work?

1. 8 km
2. 9.6 km
3. 10 km
4. 12 km

Answer: 9.6 km

At 8 km/h he is 18 minutes late, and at 12 km/h he is 6 minutes early, so the time difference between the two trips is 24 minutes = 0.4 h. Since \(d/8 - d/12 = 0.4\), we get \(d(1/24)=0.4\), hence \(d=9.6\) km.

Q6. The ratio of the speeds of a train and a truck is 5:6. If the truck covers a distance of 450 km in 5 hours, what is the speed of the train in km/h?

1. 75 km/h
2. 80 km/h
3. 85 km/h
4. 90 km/h

Answer: 75 km/h

The truck’s speed is \(450/5 = 90\) km/h. Since train:truck = 5:6, the train’s speed is \(90 \times \frac{5}{6} = 75\) km/h.

Q7. A man covered a certain distance in 3 parts with average speeds of 20 km/h, 30 km/h, and 60 km/h. What is his average speed over the entire journey, assuming equal distances?

1. 30 km/h
2. 35 km/h
3. 40 km/h
4. 45 km/h

Answer: 30 km/h

When equal distances are covered at different speeds, average speed = total distance / total time. For equal distances, this becomes the harmonic mean of the speeds. Here, average speed = 3 / (1/20 + 1/30 + 1/60) = 30 km/h.

Q8. An athlete runs a 200-meter race in 20 seconds. What is his speed in km/h?

1. 36 km/h
2. 40 km/h
3. 45 km/h
4. 30 km/h

Answer: 36 km/h

Speed = distance/time = \(200/20 = 10\) m/s. Converting to km/h: \(10 \times \frac{18}{5} = 36\) km/h.

Q9. A train 150 meters long takes 5 seconds to cross a man. What is its speed in m/s?

1. 30
2. 25
3. 20
4. 35

Answer: 30

When a train crosses a man, it covers a distance equal to its own length. So speed = 150 ÷ 5 = 30 m/s. Hence, the correct answer is 30.

Q10. A boat travels 24 km upstream and 28 km downstream in 9 hours. It also travels 30 km upstream and 21 km downstream in 10 hours. Find the speed of the boat in still water.

1. 6.50 km/h
2. 7.45 km/h
3. 10.45 km/h
4. 12 km/h

Answer: 7.45 km/h

Let the speed of the boat in still water be $b$ km/h and the speed of the stream be $s$ km/h. Then $\frac{24}{b-s}+\frac{28}{b+s}=9$ and $\frac{30}{b-s}+\frac{21}{b+s}=10$. Solving these simultaneous equations gives $b=7.45$ km/h.

Q11. An athlete runs a 400-meter race in 32 seconds. His speed in km/h is:

1. 45 km/h
2. 40 km/h
3. 48 km/h
4. 50 km/h

Answer: 45 km/h

Speed = 400/32 = 12.5 m/s. Converting to km/h: 12.5 × 18/5 = 45 km/h.

Q12. Dhiraj goes to his school from his house at a speed of 3.8 km/h and returns at 2.6 km/h. If he takes 5 hours for the round trip, the distance between his house and school is:

1. 6.79 km
2. 6.5 km
3. 7 km
4. 7.72 km

Answer: 7.72 km

If the one-way distance is \(d\), then total time is \(d/3.8 + d/2.6 = 5\). Solving gives \(d\approx 7.72\) km. So the distance between house and school is 7.72 km.

Q13. A 180 m long train runs at 72 km/h. How long will it take to cross a pole?

1. 9 sec
2. 10 sec
3. 12 sec
4. 15 sec

Answer: 9 sec

Speed = 72 km/h = 72 × 5/18 = 20 m/s. To cross a pole, the train must cover 180 m, so time = 180/20 = 9 s.

Q14. A bus travels a distance of 240 km in 4 hours. If the bus increases its speed by 20 km/h, how much time will it take to cover the same distance?

1. 3 h
2. 2.5 h
3. 3.5 h
4. 4 h

Answer: 3 h

The original speed is $240/4 = 60$ km/h. After increasing by 20 km/h, the speed becomes 80 km/h, so time taken is $240/80 = 3$ hours.

Q15. A man rows 15 km downstream in 3 hours and 9 km upstream in 3 hours. What is the speed of the stream?

1. 1 km/h
2. 2 km/h
3. 3 km/h
4. 4 km/h

Answer: 1 km/h

Downstream speed = 15/3 = 5 km/h and upstream speed = 9/3 = 3 km/h. The speed of the stream is half the difference of these speeds, i.e. (5 - 3)/2 = 1 km/h.

Q16. An express train covers a fixed distance in 40 minutes at an average speed of 200 km/h. Due to construction work, it needs to be diverted, increasing the distance by 25%. If the train needs to arrive at its destination on time in 40 minutes, what should its new average speed be in km/h?

1. 250 km/h
2. 260 km/h
3. 270 km/h
4. 280 km/h

Answer: 250 km/h

Since time remains 40 minutes, speed is directly proportional to distance. If the distance increases by 25%, the speed must also increase by 25%. Thus, new speed = $200\times 1.25 = 250$ km/h.

Q17. On a circular track, a motorcycle starts from point X and a truck starts from point Y, which is 500 m ahead of X in the direction of motion. The speed of the motorcycle is 20 m/s and that of the truck is 8 m/s. If the length of the track is 2.2 km, how much distance will the motorcycle have travelled when it overtakes the truck for the first time?

1. 845.5 m
2. 1,800 m
3. 800 m
4. 833.33 m

Answer: 833.33 m

The truck is 500 m ahead, so the initial gap is 500 m. Since the motorcycle is faster by 20−8 = 12 m/s, it must gain 2200−500 = 1700 m relative to the truck to overtake it for the first time on the circular track. Time taken = 1700/12 = 141.67 s, so motorcycle distance = 20 × 141.67 ≈ 833.33 m.

Q18. A bus travels 30% of its total route at 24 km/h and the rest at 36 km/h. What is its average speed over the whole trip?

1. 28.8 km/h
2. 29.4 km/h
3. 30 km/h
4. 31.3 km/h

Answer: 31.3 km/h

Take the total distance as 100 km. Then 30 km is covered at 24 km/h and 70 km at 36 km/h, so total time is 30/24 + 70/36 hours. Average speed equals total distance divided by total time, which gives about 31.3 km/h.