# Problems on Boats Stream

Q21. A fisher man can row 4 km against the stream in 40 minutes and return in 30 minutes. What is the speed of the current ?

(a) 1 km/h

(b) 2 km/h

(c) 3 km/h

(d) 4 km/h

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

Speed upstream = (4/40 X 60) km/h = 6 km/h

Speed downstream = (4/30 X 60) km/h = 8 km/h

Speed of the current = ½ (8 - 6) = ½ X 2 = 1 km/h

Q22. A man can row at 4 km/h in still water. If the river is running at 2 km/h, it takes him 70 minutes to row to a place and back. How far is the place ?

(a) 1½ km

(b) 1¾ km

(c) 3¼ km

(d) 3¾ km

**Answer:** (b) 1¾ km

Speed Downstream = (4 + 2) km/h = 6 km/h

Speed Upstream = (4 - 2) km/h = 2 km/h

Let the required distance be x km

∴ | x | + | x | = | 70 |

6 | 2 | 60 |

⇒ | x | + | x | = | 7 |

6 | 2 | 6 |

⇒ | x + 3x | = | 7 |

6 | 6 |

⇒ 4x = 7

⇒ x = 7/4 = 1¾

Q23. A man can row three quaters of a kilometer against the stream in 11¼ minutes and return in 7½ minutes. The speed of the man in still water

(a) 3 km/h

(b) 4 km/h

(c) 5 km/h

(d) 6 km/h

**Answer:** (c) 5 km/h

Distance covered up stream in 45/4 min = ¾ km

Distance covered upstream in 1 hour = (¾ X 4/45 X 60) = 4 km

Distance covered downstream in 15/2 min = ¾ km

Distance covered downstream in 1 hour = (¾ X 2/15 X 60) Km = 6 km

Speed of the man in still water = ½ (6 + 4) km/h = 5 km/h

Q24. A boat running upstream takes 7 hours 48 minutes to cover a certain distance while it takes 4 hours to cover the same distance running downstream. What is the ratio between speed of the boat and the speed of water current respectively ?

(a) 37 : 14

(b) 41 : 16

(c) 52 : 18

(d) 59 : 19

**Answer:** (d) 59 : 19

Let the speed of the boat be x km/h

Speed of the stream be y km/h

Now, 39/5 X (x-y) = 4(x+y)

⇒ 39(x-y) = 20(x+y)

⇒ 39x - 39y = 20x + 20y

⇒ 19x = 59y

⇒ x/y = 59/19

∴ x : y = 59 : 19

Q25. A boat goes 30 km downstream and 24 km upstream in 6 hours. It goes 39 km upstream and 26 km downstream in 6 hour 30 minutes. The speed of the boat in still water is

(a) 7.4 km/h

(b) 8.9 km/h

(c) 10.5 km/h

(d) 12.3 km/h

**Answer:** (c) 10.5 km/h

Let the speed of the boat in still water be x km/h and the speed of the stream be y km/h

Now speed upstream = (x - y) km/h

Speed downstream = (x + y) km/h

A/Q | 30 | + | 24 | = 6 -------- (1) |

x + y | x - y |

And | 26 | + | 39 | = | 13 |

x + y | x - y | 2 |

⇒ | 2 | + | 3 | = 1 ---------(2) |

x + y | x - y | 2 |

putting 1/(x+y) = a, 1/(x-y) = b in (1) and (2)

(1) ⇒ 30a + 24b = 6 ⇒ 5a + 4b = 1 ------- (3)

(2)⇒ 2a + 3b = ½

⇒ 4a + 6b = 1 -------(4)

(3) X 4 ⇒ 20a + 16b = 4 ------ (a)

(4) X 5 ⇒ 20a + 30b = 5 ------- (b)

(a) -(b)⇒ -14b = -1

⇒ b = 1/14 ⇒ 1/(x-y) = 1/14 ⇒ x - y = 14 ------ (5)

(3)⇒ 5a + 4 X (1/14) = 1

⇒ 5a + 2/7 = 1

⇒ 5a = 1 - 2/7 = 5/7

⇒ a= 1/7

⇒ 1/(x+y) = 1/7 ⇒ x+ y = 7 ------ (6)

(5) + (6) ⇒ 2x = 21 ⇒ x = 10.5

∴ the speed of the boat in still water = 10.5 km/h

Q26. A boatman goes 2 km against the current of stream in 30 minutes and return to the same spot in 20 minutes. What is his rate of rowing in still water ?

(a) 5 km/h

(b) 7 km/h

(c) 12 km/h

(d) 13 km/h

**Answer:** (a) 5 km/h

Speed upstream = (2/30) X 60 km/h = 4 km/h

Speed downstream = (2/20) X 60 km/h = 6 km/h

Speed in still water = ½ (6 + 4) Km/h = 5 km/h

Q27. The speed of a boat in still water is 14 km/h. It can go 30 km upstream and return downstream to the original point in 5 hour. The speed of the stream is

(a) 4 km/h

(b) 6 km/h

(c) 7 km/h

(d) 8 km/h

**Answer:** (a) 4 km/h

Let the speed of the stream be x km/h

speed upstream = (14 - x) km/h

speed downstream = (14 + x) km/h

30 | + | 30 | = 5 | |

14 - x | 14 + x |

⇒ | 450 + 30x + 450 - 30x | = 5 |

(14 + x)(14 - x) |

⇒ | 900 | = 5 |

14^{2} - x^{2} |

⇒ 900 = 5(196 - x^{2})

⇒ 900 = 980 - 5x^{2}

⇒ 5x^{2} = 80

⇒ x^{2} = 16

⇒ x^{2} = 4^{2}

⇒ x = 4

∴ Speed of the stream = 4 km/h

Q28. A boat running downstream covers 24 km in 4 hr, while for covering the same distance upstream it takes 6 hours. What is the speed of the boat in still water ?

(a) 3 km/h

(b) 5 km/h

(c) 6 km/h

(d) 9 km/h

**Answer:** (b) 5 km/h

Speed downstream = 24/4 = 6 km/h

Speed upstream = 24/6 = 4 km/h

Speed of the boat in still water = ½ (6 + 4) km/h = 5 km/h

Q29. A steamer goes downstream from one port to another in 4 hours. It covers the same distance upstream in 5 hours. If the speed of the stream is 2 km/h, the distance between the two ports is

(a) 52 km

(b) 55 km

(c) 65 km

(d) 80 km

**Answer:** (d) 80 km

Let the distance between the two ports be x km

∴ Speed downstream = x/4 km/h

Speed upstream = x/5 km/h

Speed of the stream = ½ (x/4 - x/5)

A/Q ½ ( | x | - | x | ) = 2 |

4 | 5 |

⇒ | x | - | x | = 4 |

4 | 5 |

⇒ | 5x - 4x | = 4 |

20 |

⇒ x = 80 km

Q30. A boat goes 20 km downstream in 10 hours, It takes 2 hours more to cover the same distance against the stream. What is the speed of the boat in still water ?

(a) 1.52 km/h

(b) 1.83 km/h

(c) 2.15 km/h

(d) 2.77 km/h

**Answer:** (b) 1.83 km/h

Speed downstream = 20/10 km/h = 2 km/h

Speed upstream = 20/12 km/h = 1.66 km/h

Speed of the boat in still water = ½ (2 + 1.66) km/h = ½ X 3.66 = 1.83 km/h

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