Important for :

1

C

Let Distance = D km, Speed = S km/hTime = | Distance |

Speed |

40 = | Distance | .... (1) |

Speed |

After reducing speed,

Distance = Distance – 5 km, Speed = S × | 14 | km/h |

15 |

Time = | Distance |

Speed |

40 = | (Distance – 5) | .... (2) | |

Speed × | 14 | ||

15 |

After solving equation 1 and 2

Distance | = | (Distance – 5) | |

Speed | Speed × | 14 | |

15 |

14 Distance = 15 (Distance – 5)

14 Distance = 15 Distance – 75

Distance = 75 km.

Hence, option C is correct.

2

C

Let the speed of auto be x kmph= | 6 x | = 4x |

1.5 |

As per the given information,

Time taken by auto + Time taken by train + Time taken by bike = 21 hours

⇒ | 132 | + | 852 | + | 248 | = 21 |

x | 6x | 4x |

or, | 132 | + | 142 | + | 62 | = 21 |

x | x | x |

or, 21x = 132 + 142 + 62 = 336

∴ x = |
336 | = 16 |

21 |

Hence, option C is correct.

3

D

Average speed = | total distance | |

total time |

Total distance = 50 + 130 = 180 miles

∴ Total time = |
180 | = 4 hours. |

45 |

Time spent for the first 50 miles = | 50 | = 2 hours |

25 |

∴ Average speed for the remaining 130 miles = |
130 | = 65 mph |

2 |

Hence, option D is correct.

4

E

Since different speeds are traveled for equal distance, the average speed can be found outAverage speed = | (2 × 30 × 50) | = | 300 | km/h |

(30 + 50) | 8 |

Distance covered = | 300 | × 16 = 600 km | |

8 |

Hence, option E is correct.

5

D

The distance covered by X in 2 hours is 2 × 60 = 120 km

The distance remaining is 1080 km

This distance travelled before meeting is directly proportional to their speed

They meet 360 km from B. Hence, train Y must've travelled 360 km

X has travelled 720 km and Y has travelled only 360 km in the same time

This means that speed of X is twice of Y

Since speed of X is 60 kmph therefore speed of Y is 30 kmph

Hence, option D is correct.

The distance remaining is 1080 km

This distance travelled before meeting is directly proportional to their speed

They meet 360 km from B. Hence, train Y must've travelled 360 km

X has travelled 720 km and Y has travelled only 360 km in the same time

This means that speed of X is twice of Y

Since speed of X is 60 kmph therefore speed of Y is 30 kmph

Hence, option D is correct.