Important for :

1

2

D

Speed of the man in still water = 12 km/hrSpeed of the stream = 3 km/hr

Speed downstream = (12 + 3) = 15 km/hr

Speed upstream = (12 – 3) = 9 km/hr

Let the distance travelled be ‘d’ km Then

Average Speed = | total distance |

total time |

= | d + d | ||

d | + | d | |

15 | 9 |

= | 2d |

9d + 15 d | |

15 × 9 |

= | 2d × (15 × 9) | = | 45 | km/hr | = 11 | 1 | km/hr |

24d | 4 | 4 |

Hence, option (D) is correct.

3

B

Let the speed of boat in still water = 16x, speed of stream = 5xUpstream speed = 16x – 5x = 11x

S = | D |

t |

11x = | 16.5 | × 60 |

45 |

x = 2

speed of boat in still water = 32 km/h, speed of stream = 10 km/h

Downstream speed = 32 + 10 = 42 km/h

Distance = 17.5 km

time = | 17.5 |

42 |

= | 5 | hour |

12 |

or | 5 | × 60 = 25 minutes |

12 |

Hence, option B is correct.

4

D

Ratio of speed of boat in downstream and speed of stream is 9 : 1

Given Speed of current = 3 km/ h

Speed of boat in downstream = 9 × 3 = 27 km/h

Speed of boat in still water = Speed of boat in downstream – Speed of current

= 27 – 3 = 24 km/h

Speed of boat in upstream = 24 – 3 = 21 km/h

Distance travelled by boat in upstream in 5 hours = 21 × 5 = 105 km

Hence, option D is correct.

5

B

For the first boat let the speed of the stream be 5x and the speed of the boat be 7x.

For the 2^{nd} boat, let the speed of the stream be 6y and the speed of the 2^{nd} boat be 8y.

The speed of the stream will be the same.

For the 2

The speed of the stream will be the same.

or, x = | 6 | y |

5 |

Now, the required ratio of the speed of the first boat to that of the second boat = 7x : 8y

⇒ 7 × | 6 | y : 8y |

5 |

[Putting x in terms of y]

∴ |
21 | y : 4y = 21 : 20 |

5 |

Hence, option B is correct.