## 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**

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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

Question 11 |

Length of the platform is 100 meters, if a train running at a speed of 90 m/sec, crosses the platform in 2 sec. What is the length of the train?

100 m | |

80 m | |

120 m | |

90 m |

**Trains, Boats and Streams**

**Discuss it**

Question 11 Explanation:

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

Question 12 |

In what time will a train running at a speed of 90 m/sec, of length 80 meters crosses a platform of length 100 meters?

4 sec | |

5 sec | |

2.5 sec | |

2 sec |

**Trains, Boats and Streams**

**Discuss it**

Question 12 Explanation:

relative distance = 80+100
V = D/T
90 =( 180)/t = 180/90 = 2sec

Question 13 |

Two trains T1 and T2 start from two stations A and B, at the same time with speed 60 meters/sec and 40 meters/sec respectively. Stations are 100 meters apart from each other. At what distance from station A will they meet?

60 m | |

40 m | |

80 m | |

70 m |

**Trains, Boats and Streams**

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Question 13 Explanation:

A -------------------------- | ------------------ B
<---------- x --------------><---(100-x)----->
60t 40t
x = 60t
100-x = 40t
x = 60 meters from A

Question 14 |

Two trains T1 and T2 start from two stations A and B, at the same time with speed 60 meters/sec and 40 meters/sec respectively. Stations are 100 meters apart from each other. At what time will they meet?

2 sec | |

2.5 sec | |

1.5 sec | |

1 sec |

**Trains, Boats and Streams**

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Question 14 Explanation:

A -------------------------- | ------------------ B
<---------- x -------------><---(100-x)------>
60t 40t
x = 60t
100-x = 40t
100-60t =40t
t = 1sec

Question 15 |

Two trains are running in the same direction on two parallel tracks at 40 m/sec and 60 m/sec. How much time will it take to cross the slower train by faster train if the length of slower train in 50 meter and that of faster train is 20 meter? (Assume initially faster train was far behind the slower train).

5 sec | |

10 sec | |

4 sec | |

3.5 sec |

**Trains, Boats and Streams**

**Discuss it**

Question 15 Explanation:

Sol: relative speed = 60 - 40 = 20 m/sec
relative length = 70 meters
time = D/V = 70/20 = 3.5 sec

There are 15 questions to complete.