a. 3 km/hr

b. 3.5 km/hr

c. 4 km/hr

d. 6 km/hr

**Answer:** c. 4 km/hr

**Explanation:**

Man's/Boat's Speed = X

Stream/Current/River Speed = Y

∴ Downstream speed = X + Y

Upstream speed = X - Y

∴ X+Y = 4.5+1.5 = 6 km/hr and X-Y = 4.5-1.5 = 3 km/hr

Let distance be D km

Downstream Time | = | Distance | = | D |

Speed | 6 |

Upstream Time | = | D |

3 |

Average Speed | = | Total Distance | = | D+D | = | 6 x 2D | = | 4 km/hr |

Time taken | D/6+D/3 | 3D |

a. 20 km

b. 72 km

c. 80 km

d. 96 km

**Answer:** d. 96 km

**Explanation:**

Man's/Boat's Speed = X

Stream/Current/River Speed = Y

∴ Downstream speed = X + Y

Upstream speed = X - Y

X+Y = 10+2 = 12 km/hr and X-Y = 10-2 = 8 km/hr

Let Time be T hours for downstream

Distance is same

∴ D = D

∴ 12 x T = 8 x (T+4)

∴ T = 8 hours = Time for downstream

a. 4 km/hr ; 16 km/hr

b. 5 km/hr ; 15 km/hr

c. 6 km/hr ; 14 km/hr

d. 8 km/hr ; 12 km/hr

**Answer:** b. 5 km/hr ; 15 km/hr

**Explanation:**

Man's/Boat's Speed = X

Stream/Current/River Speed = Y

∴ Downstream speed = X + Y

Upstream speed = X - Y

Downstream Speed | = | Distance covered | = | 20 | = | 20 km/hr |

Time taken | 1 |

Upstream Speed | = | 20 | = | 10 km/hr |

2 |

Adding them we get,

X+Y+X-Y = 30 km/hr

Y=20-15 = 5 km/hr = Speed of river

a. 2 hours 30 minutes

b. 2 hours 40 minutes

c. 3 hours 10 minutes

d. 4 hours

**Answer:** b. 2 hours 40 minutes

**Explanation:**

Stream/Current/River Speed = Y

∴ Downstream speed = X + Y

Upstream speed = X - Y

X+Y = (45+Y) km/hr

1 hour 20 minutes = 1 hour | + | 20 | = | 4 | hours |

60 | 3 |

Downstream Speed | = | Distance covered |

Time taken |

∴ 45+Y | = | 80 | = | 60 |

4/3 |

X-Y = 45-15 = 30 km/hr

Time taken to go against the stream | = | 80 | hrs = 2 hours 40 minutes |

30 |

a. 2 km/hr

b. 3 km/hr

c. 4 km/hr

d. 6 km/hr

**Answer:** a. 2 km/hr

**Explanation:**

Stream/Current/River Speed = Y

∴ Downstream speed = X + Y

Upstream speed = X - Y

Downstream time | = | Distance | = | 24 |

speed | X+Y |

Upstream time | = | Distance | = | 36 |

speed | X-Y |

24 | + | 36 | = 6 ½ hours = | 13 | hours ----------------(1) |

X+Y | X-Y | 2 |

Similarly in 2

36 | + | 24 | = 6 hours ----------------(2) |

X+Y | X-Y |

Multiply equation (1) by 2 and equation (2) by 3 and then subtracting equation (1) from (2)

3 x 36 | - | 2 x 24 | = 3 x 6 - | 2 x 13 |

X+Y | X+Y | 2 |

∴ | 108 | - | 48 | = 5 |

X+Y | X+Y |

36 | + | 24 | = 6 -------------Putting value of X+Y in equation (2) |

12 | X-Y |

(X+Y) - (X-Y) = 12-8 = 4