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## Arithmetic: Time Speed Distance Test-6

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Question 1 |

A pilot flies an aircraft at a certain speed for a distance of 800 km. He could have saved 40 min by increasing the average speed of the plane by 40 km/h. Find the average speed of the aircraft.

200 km/h | |

300 km/h | |

240 km/h | |

None of these |

Question 1 Explanation:

Let the average speed of the aircraft = s km/h

Distance = 800 km

Therefore time taken by the aircraft (t) = 800/s……………………………1

According to question, he could have saved 40 min by increasing the average speed of the plane by 40 km/h

So we can say that

(t - 2/3) = 800/(s+40)…………………………………………………2

From both the equations we can say that

800/s = 800/(s+40) + 2/3

Solving for s, we get

s = 200 km/h

Distance = 800 km

Therefore time taken by the aircraft (t) = 800/s……………………………1

According to question, he could have saved 40 min by increasing the average speed of the plane by 40 km/h

So we can say that

(t - 2/3) = 800/(s+40)…………………………………………………2

From both the equations we can say that

800/s = 800/(s+40) + 2/3

Solving for s, we get

s = 200 km/h

Question 2 |

An Auto travels 10 km/h faster than a Scooty for a journey of 1000 km. The Scooty takes 5 h more than the Auto to complete the journey. Find the speed of the Scooty.

40 km/h | |

70 km/h | |

50 km/h | |

None of these |

Question 2 Explanation:

Let us assume that the speed of the scooty = s km/h

Therefore time taken by the scooty = 1000/s………………………………1

Speed of auto = s + 10

We are given that: the Scooty takes 5 h more than the Auto

So we can say that

1000/(s+10) = (1000/s) - 5………………………………………….2

Using the options in to solve this equations, we see option (a) fits perfectly.

Therefore time taken by the scooty = 1000/s………………………………1

Speed of auto = s + 10

We are given that: the Scooty takes 5 h more than the Auto

So we can say that

1000/(s+10) = (1000/s) - 5………………………………………….2

Using the options in to solve this equations, we see option (a) fits perfectly.

Question 3 |

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

11 km/hr | |

12 km/hr | |

13 km/hr | |

14 km/hr |

Question 3 Explanation:

Let’s suppose that the time taken by man at 10km/h to cover the distance by 1 pm = t h

Now at speed of 15km/h the time taken = (t-2) h

Now the distance covered is same so we can say that

10(t) = 15(t-2)

t= 6

Therefore the distance covered will be = 10 x 6 = 60

Therefore the speed at which the man has to travel to reach the place at noon = 60/(t-1) = 60/5 = 12 km/h

Now at speed of 15km/h the time taken = (t-2) h

Now the distance covered is same so we can say that

10(t) = 15(t-2)

t= 6

Therefore the distance covered will be = 10 x 6 = 60

Therefore the speed at which the man has to travel to reach the place at noon = 60/(t-1) = 60/5 = 12 km/h

Question 4 |

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/h. The other one walks at 5.4 km/h. The train needs 8.4 and 8.5 s respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

66 km/h | |

72 km/h | |

78 km/h | |

81 km/h |

Question 4 Explanation:

Let’s suppose that the speed of the train be = s km/h

We are given the information that both the persons are walking in the same direction of the train

So (s – 4.5)x 8.4 = (s – 5.4)x 8.5

0.1s = 8.1

S= 81 km/h

We are given the information that both the persons are walking in the same direction of the train

So (s – 4.5)x 8.4 = (s – 5.4)x 8.5

0.1s = 8.1

S= 81 km/h

Question 5 |

Two trains move from station Ladii and station Pamma towards each other at the speed of 50 km/h and 60 km/h. At the meeting point, the driver of the second train felt that the train has covered 120 km more. What is the distance between Ladii and Pamma ?

1320 km | |

1100 km | |

1200 km | |

960 km |

Question 5 Explanation:

At the meeting point, the driver of the second train felt that the train has covered 120 km more.

So if the distance travelled by train from Laddi = d km

Then the distance travelled by from Pamma = (d+120) km

Since the time for both the trains are same so we can say that d/50 = (d+120)/60

by solving this we will get the distance (d) = 600

so the total distance covered by the train = d + (d+120)= 1320 km

So if the distance travelled by train from Laddi = d km

Then the distance travelled by from Pamma = (d+120) km

Since the time for both the trains are same so we can say that d/50 = (d+120)/60

by solving this we will get the distance (d) = 600

so the total distance covered by the train = d + (d+120)= 1320 km

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