# Problems on Boats Stream

Q11. A boat goes 9 km in an hour in still water. It takes thrice as much time in covering the same distance against the current. Speed of the current is

(a) 6 km/hr

(b) 8 km/hr

(c) 9 km/hr

(d) 10 km/hr

**Answer:** (a) 6 km/hr

Speed in still water = 9 km/hr

Speed against the current = 9/3 km/hr = 3 km/hr

Let the speed of the current be x km/hr

∴ 9-x = 3 => x = 9 - 3 = 6 km/hr

Q12. A man rows 40 km downstream and 22 km upstream taking 5 hours each time. What is the velocity of the current ?

(a) 1.8 km/h

(b) 1.9 km/h

(c) 2.3 km/h

(d) 2.7 km/h

**Answer:** (a) 1.8 km/h

Downstream speed = 40/5 km/h = 8 km/h

Upstream speed = 22/5 km/h = 4.4 km/h

∴ velocity of the current = 1/2 (8 - 4.4) km/h = 1/2 X 3.6 km/h = 1.8 km/h

Q13. A man rows 42 km down stream in 7 hours and 15 km upstream in 5 hours. What is the velocity of the current ?

(a) 1.3 km/h

(b) 1.5 km/h

(c) 2.2 km/h

(d) 2.5 km/h

**Answer:** (b) 1.5 km/h

Downstream speed = 42/7 km/h = 6 km/h

Upstream speed = 15/5 km/h = 3 km/h

∴ velocity of the current = ½ (6 - 3) km/h = ½ X 3 km/h = 1.5 km/h

Q14. A man can row 8 km/h in still water. When the river is running at 2 km/h, it takes him 4 hours to row to a place and back. How far is the place ?

(a) 9 km

(b) 11 km

(c) 12 km

(d) 15 km

**Answer:** (d) 15 km

Speed downstream = (8 + 2) km/h = 10 km/h

Speed upstream = (8 - 2) km/h = 6 km/h

Let the required distance be x Km

∴ | x | + | x | = 4 |

10 | 6 |

⇒ | 3x + 5x | = 4 |

30 |

⇒ 8x = 4 X 30

⇒ x = (4 X 30)/8 = 15 km

Q15. A boat is rowed downstream at 15.5 km/h and upstream at 8 km/h. The speed of the stream is

(a) 2.19 km/h

(b) 3.75 km/h

(c) 4.12 km/h

(d) 4.33 km/h

**Answer:** (b) 3.75 km/h

Speed of the stream = ½(15.5 - 8) km/h = ½ X 7.5 km/h = 3.75 km/h

Q16. The speed of a motor boat is that of the current of water as 36:4. The boat goes along with the current in 4 hours 30 minutes. It will come back in

(a) 3(5/7) hr

(b) 3(1/5) hr

(c) 4(5/7) hr

(d) 5(5/8) hr

**Answer:** (d) 5(5/8) hr

Let, the speed of the motor boat be 36x km/h

and the speed of the current of water be 4x km/h

∴ Speed downstream = (36x + 4x) km/h = 40x km/h

Speed upstream = (36x - 4x) km/h = 32x km/h

Distance covered in downstream = (40x X 9/2) km = 180x km

In upstream,

32x km covered in 1 hr

∴ 180x km covered in = (1/32x) X 180x hr = 180/32 hr = 5(20/32) hr = 5(5/8) hr

Q17. A man can row upstream at 5 km/hr and downstream at 10 km/hr. Find the man's rate in still water.

(a) 5.5 km/h

(b) 6.5 km/h

(c) 7.5 km/h

(d) 8.5 km/h

**Answer:** (c) 7.5 km/h

Upstream speed = 5 km/h

Downstream speed = 10 km/h

∴ Rate in still water = ½ (10 + 5) km/h = 7.5 km/h

Q18. A boat takes one fourth time in moving a certain distance downstream than upstream. What is the ratio between rate in still water and rate of current ?

(a) 3 : 7

(b) 4 : 5

(c) 5 : 3

(d) 6 : 5

**Answer:** (c) 5 : 3

Let the speed of the boat in still water = u km/h

And the speed of the current be v km/h

Rate downstream = (u + v) km/h

Rate upstream = (u - v) km/h

Let the distance be x km

Now | 4x | = | x |

u + v | u - v |

⇒ 4u - 4v = u + v

⇒ 3u = 5v

⇒ u/v = 5/3

∴ Required ratio = 5 : 3

Q19. A man can row 6½ kms an hour in still water and he finds that it takes him twice as long to row down the river. The rate of the stream is

(a) 2(1/6) km/h

(b) 3(1/5) km/h

(c) 3(1/7) km/h

(d) 4(1/5) km/h

**Answer:** (a) 2(1/6) km/h

Let the rate of the stream be x km/h

∴ Speed downstream = (13/2 + x) km/h

Speed upstream = (13/2 - x) km/h

A/Q ( | 13 | + x ) = 2 ( | 13 | - x) |

2 | 2 |

⇒ | 13 | + x = 13 - 2x |

2 |

⇒ 3x = 13 - (13/2) = 13/2

⇒ x = 13/(2X3) = 13/6 = 2(1/6) km/h

Q20. A boat covers a distance of 30 km in 2½ hrs running downstream. While returning it covers the same distance in 3¾ hrs. What is the speed of the boat in still water.

(a) 6 km/h

(b) 7 km/h

(c) 8 km/h

(d) 10 km/h

**Answer:** (d) 10 km/h

Speed Downstream = (30 X (2/5)) km/h = 12 km/h

Speed Upstream = (30 X (4/15)) km/h = 8 km/h

∴ Speed of boat in still water = ½ (12 + 8) km/h = 10 km/h