## Trains, Boats and Streams

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Question 1 |

A boatman takes 3 hours 45 minutes to travel 15 km downstream and takes 2 hours 30 minutes to travel 5 km upstream of a river. What is the speed of the stream of the river in km/h?

2 km/h | |

1 km/h | |

6 km/h | |

4 km/h |

**Trains, Boats and Streams**

**Discuss it**

Question 1 Explanation:

Downstream:
Time taken = 3 + 45/60 = 3 + 3/4 = 15/4 h.
Distance covered = 15 km.
Downstream Speed = 15 / (15/4) = 4 km/h.
Upstream:
Time taken = 2 + 30/60 = 2 + 1/2 = 5/2 h.
Distance covered = 5 km.
Upstream Speed = 5 / (5/2) = 2 km/h.
We know, speed of stream = 1/2 (Downstream Speed - Upstream Speed) = 1/2 (4-2) = 1 km/h.

Question 2 |

A speedboat runs 6 km upstream in a river and comes back to the starting point in 33 minutes. The stream of the river is running at 2 km/hr. What is the speed of speedboat in still water?

25 km/h | |

21 km/h | |

26 km/h | |

22 km/h |

**Trains, Boats and Streams**

**Discuss it**

Question 2 Explanation:

Let the speed of speedboat in still water be x km/h.
Then, speed downstream = (x + 2) km/h, speed upstream = (x - 2) km/h.
Since it goes 6 km upstream and comes back in 33 minutes, we have
6/(x+2) + 6/(x-2) = 33/60
⇒ 11x² - 240x - 44 = 0
⇒ 11x² - 242x + 2x - 44 = 0
⇒ (x - 22)(11x + 2) = 0
⇒ x = 22.
Therefore, the required speed = 22 km/h.

Question 3 |

A boat runs at the speed of 13 km/h in still water. If the speed of the stream is 4 km/h, how much time will it take to go 68 km downstream?

5 h | |

4 h | |

6 h | |

3 h |

**Trains, Boats and Streams**

**Discuss it**

Question 3 Explanation:

Speed of the boat downstream = 13 + 4 = 17 km/h.
Therefore, time taken to go 68 km downstream = (68/17) = 4 h.

Question 4 |

Peter's speedboat run at a speed of 9 km/h in still water. He rows to a place at a distance of 105 km and comes back to the starting point. If the speed of stream is 1.5 km/h, find out the time taken by Peter.

24 h | |

21 h | |

23 h | |

22 h |

**Trains, Boats and Streams**

**Discuss it**

Question 4 Explanation:

Upstream speed = 9 - 1.5 = 7.5 km/h.
Downstream speed = 9 + 1.5 = 10.5 km/h.
Therefore, time taken = 105/7.5 + 105/10.5 = 14 + 10 = 24 h.

Question 5 |

A motorboat crosses a certain distance in 1 hour and comes back in 1½ hours. If the stream is running at 3 km/h, find out the speed of motorboat in still water.

10 km/h | |

15 km/h | |

12 km/h | |

None of these |

**Trains, Boats and Streams**

**Discuss it**

Question 5 Explanation:

Let the speed of motorboat in still water be x km/h. Then,
Downstream speed = (x + 3) km/h.
Upstream speed = (x - 3) km/h.
Then, (x + 3) × 1 = (x - 3) × 3/2
⇒ 2x + 6 = 3x - 9
⇒ x = 15.
So, the speed of motorboat in still water is 15 km/h.

Question 6 |

A train crosses a pole in 20 sec. If the length of train is 500 meters, what is the speed of the train?

27 m/s | |

20 m/s | |

25 m/s | |

30 m/s |

**Trains, Boats and Streams**

**Discuss it**

Question 6 Explanation:

V = 500/20 = 25 m/sV = 500/20 = 25 m/s

Question 7 |

A train crosses a pole in 10 sec. If the length of train is 100 meters, what is the speed of the train in Kmph?

34 | |

36 | |

30 | |

32 |

**Trains, Boats and Streams**

**Discuss it**

Question 7 Explanation:

V = 100/10 = 10 m/s = 10*3600/1000 = 36Km/hr

Question 8 |

A train is running at a speed of 100Kmph. A car is running on road parallel to the train’s track at a speed of 20 Kmph in the same direction as of train. How much time will it take to cross the car if the length of the train is 100 meters?

5 sec | |

4 sec | |

5.5 sec | |

4.5 sec |

**Trains, Boats and Streams**

**Discuss it**

Question 8 Explanation:

Relative speed of train = 100-20 Kmph (say car is stopped)
T = D/V = 0.100/80 = .00125 hrs
=> 00125*3600 = 4.5 secs

Question 9 |

A train is running at a speed of 100Kmph. A car is running on road parallel to the train’s track at a speed of 20 Kmph opposite to train. How much time will it take to cross the car if the length of the train is 100 meters?

5 sec | |

4 sec | |

3 sec | |

3.5 sec |

**Trains, Boats and Streams**

**Discuss it**

Question 9 Explanation:

Relative speed of train = 100+20 Kmph (say car is stopped)
T = D/V = 0.100/120 = .000833 hrs
=> 000833*3600 = 3 secs

Question 10 |

What is the length of the platform, if a train running at a speed of 90 m/sec and length is 80 meters, crosses the platform in 2 sec?

120 m | |

150 m | |

125 m | |

100 m |

**Trains, Boats and Streams**

**Discuss it**

Question 10 Explanation:

relative distance = L+80
V = D/T
90 =( L+80)/2 = 100 meters

There are 15 questions to complete.