=

= where

B ---> speed of boat in still water

R---->speed of current

( By componendo and dividendo)

A) 12 km/hr, 3 km/hr | B) 9 km/hr, 3 km/hr |

C) 8 km/hr, 2 km/hr | D) 9 km/hr, 6 km/hr |

Explanation:

Let the speed of the boat = p kmph

Let the speed of the river flow = q kmph

From the given data,

$\mathbf{2}\mathbf{}\mathbf{x}\mathbf{}\frac{\mathbf{28}}{\mathbf{p}\mathbf{}\mathbf{+}\mathbf{}\mathbf{q}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{28}}{\mathbf{p}\mathbf{}\mathbf{-}\mathbf{}\mathbf{q}}$

=> 56p - 56q -28p - 28q = 0

=> 28p = 84q

=> p = 3q.

Now, given that if

$\frac{\mathbf{28}}{\mathbf{3}\mathbf{q}\mathbf{}\mathbf{+}\mathbf{}\mathbf{2}\mathbf{q}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{28}}{\mathbf{3}\mathbf{q}\mathbf{}\mathbf{-}\mathbf{}\mathbf{2}\mathbf{q}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{672}}{\mathbf{60}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{28}{5\mathrm{q}}+\frac{28}{\mathrm{q}}=\frac{672}{60}\phantom{\rule{0ex}{0ex}}\mathbf{=}\mathbf{}\mathbf{}\mathbf{q}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}\mathbf{}\mathbf{kmph}\phantom{\rule{0ex}{0ex}}\mathbf{=}\mathbf{}\mathbf{}\mathbf{x}\mathbf{}\mathbf{}\mathbf{=}\mathbf{3}\mathbf{q}\mathbf{}\mathbf{=}\mathbf{}\mathbf{9}\mathbf{}\mathbf{kmph}$

Hence, **the speed of the boat = p kmph = 9 kmph and the speed of the river flow = q kmph = 3 kmph.**

A) 2 kmph | B) 4 kmph |

C) 6 kmph | D) 8 kmph |

Explanation:

Let the distance in one direction = k kms

Speed in still water = 4.5 kmph

Speed of river = 1.5

Hence, speed in upstream = 4.5 - 1.5 = 3 kmph

Speed in downstream = 4.5 + 1.5 = 6 kmph

Time taken by Rajesh to row upwards = k/3 hrs

Time taken by Rajesh to row downwards = k/6 hrs

Now, required **Average speed** =$\frac{\mathbf{Total}\mathbf{}\mathbf{distance}}{\mathbf{Total}\mathbf{}\mathbf{speed}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{2}\mathbf{k}}{{\displaystyle \frac{\mathbf{k}}{\mathbf{3}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{k}}{\mathbf{6}}}}\mathbf{}\phantom{\rule{0ex}{0ex}}=\frac{2\mathrm{k}\mathrm{x}18}{6\mathrm{k}+3\mathrm{k}}=\mathbf{4}\mathbf{}\mathbf{kmph}$

Therefore, the average speed of the whole journey =** 4kmph.**

A) Only A and B | B) Only B and C |

C) All are required | D) Any one pair of A and B, B and C or C and A is sufficient |

Explanation:

Let distance between A & B = d km

Let speed in still water = x kmph

Let speed of current = y kmph

from the given data,

d/x = 2

From A) we get d

From B) we get d/x+y

From C) we get y

So, Any one pair of A and B, B and C or C and A is sufficient to give the answer i.e, the speed of upstream.

A) 5:1 | B) 3:1 |

C) 4:1 | D) 2:1 |

Explanation:

Let the speed of the man in still water = **p** kmph

Speed of the current = **s** kmph

Now, according to the questions

**(p + s) x 10 = (p - s) x 15**

2p + 2s = 3p - 3s

**=> p : s = 5 : 1**

Hence, ratio of his speed to that of current** = 5:1.**

A) 4 kmph | B) 6 kmph |

C) 3 kmph | D) 2 kmph |

Explanation:

Let the speed of current = **'C'** km/hr

Given the speed of boat in still water = 6 kmph

Let **'d'** kms be the distance it covers.

According to the given data,

Boat takes thrice as much time in going the same distance against the current than going with the current

i.e, $\frac{\mathbf{d}}{\mathbf{8}\mathbf{}\mathbf{-}\mathbf{}\mathbf{C}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}\mathbf{}\mathbf{\times}\mathbf{}\frac{\mathbf{d}}{\mathbf{8}\mathbf{}\mathbf{+}\mathbf{}\mathbf{C}}$

$\Rightarrow 24-3\mathrm{C}=8+\mathrm{C}\phantom{\rule{0ex}{0ex}}\Rightarrow 4\mathrm{C}=16\phantom{\rule{0ex}{0ex}}\mathbf{\Rightarrow}\mathbf{}\mathbf{C}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}\mathbf{}\mathbf{kmph}$

Hence, the speed of the current **C = 4 kmph.**

A) 1 : 3 | B) 3 : 2 |

C) 2 : 3 | D) 3 : 1 |

Explanation:

Let the speed of the boat in still water is 'w'

Speed of the current is 'c'

Let the distance between two places is 'd'

According to the question, motorboat takes half time to cover a certain distance downstream than upstream.

$\frac{\mathbf{d}}{\mathbf{w}\mathbf{+}\mathbf{c}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{\mathbf{2}}\left(\frac{{\displaystyle \mathbf{d}}}{{\displaystyle \mathbf{w}\mathbf{-}\mathbf{c}}}\right)$

=> 2w - 2c = w + c

=> w = 3c

=> c : w = 1 : 3

Hence, the ratio between rate of current(c) and rate of boat in still water(w) = **1 : 3**

A) 2.8 hrs | B) 2.7 hrs |

C) 2.6 hrs | D) 2.5 hrs |

Explanation:

Let Speed of boat in still water = **b**

Let Speed of still water =** w**

Then we know that,

Speed of Upstream = **U = boat - water**

Speed of Downstream = **D = boat + water**

Given, **U + D = 82**

b - w + b + w = 82

2b = 82

=> **b = 41 kmph**

From the given data,

**41 - w = 105/3 = 35**

w = 6 kmph

Now,

**b + w = 126/t**

=> 41 + 6 = 126/t

=> **t = 126/47 = 2.68 hrs.**

A) 7:4 | B) 11:4 |

C) 4:7 | D) 8:3 |

Explanation:

Let the speed of the boat upstream be p kmph and that of downstream be q kmph

Time for upstream = 8 hrs 48 min = $8\frac{4}{5}$hrs

Time for downstream = 4 hrs

Distance in both the cases is same.

=> p x $8\frac{4}{5}$= q x 4

=> 44p/5 = 4q

=> q = 11p/5

Now, the required ratio of Speed of boat : Speed of water current

= $\frac{\mathbf{q}\mathbf{+}\mathbf{p}}{\mathbf{2}}\mathbf{:}\frac{\mathbf{q}\mathbf{-}\mathbf{p}}{\mathbf{2}}$

=> (11p/5 + p)/2 : (11p/5 - p)/2

=> 8 : 3