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# Arithmetic Aptitude :: Time and Distance

Home > Arithmetic Aptitude > Time and Distance > General Questions

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21. Hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely3. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?

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Explanation:

Here is no explanation for this answer

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22. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:

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Explanation:

Let Abhay's speed be x km/hr.

So 30/x - 30/2x = 3
=> 6x = 30

x = 5 km/hr.

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23. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?

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Explanation:

find the relative speed of the thief and policeman = (11-10)km/hr = 1 km/hr

Distance covered in 6 minutes = (1/60)*6=1/10km => 100meters

So distance between them after 6 minutes = (200-100)=100 meters

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24. A man reaches his office 30 min late, if he walks from his home at 3 km per hour and reaches 40 min early if he walks 4 km per hour. How far is his office from his house?

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Explanation:

Lets assume distance between office and his house =x km
Time taken when speed is 3 kmph = x/3 min.
Time taken when speed is 4 kmph = x/4 min.
Difference between time taken 40-(-30) = 70mins = 70/60 hours.
x/3- x/4 = 70/60
x/12= 7/6
x=14 km

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25. City bus runs two bus from A to B each making 5 round trips in a day. There are no stops between. These buses ply back and forth on same route at diff. but uniform speed. Each bus start at 7 am from respective terminus. They meet for the first time at 7 km from A. Their next meeting is at distance of 4 km from B, while travelling in opposite direction. Assuming that time by buses at terminus is negligibly small, and cost of running a bus is 20 per km. Find daily cost of buses ?

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Explanation:

Let's assume total distance travelled by both bus = x km
So as per question

First meet at 7 km from A.
By that time first bus travels 7 Km and second one travels x-7 Km. As they have travelled for the same time,

Second meeting is at 4 km from B:
By that time first bus travels (x+4) Km and second bus will travels x+(x-4) = (2x-4) km.
=> 7/(x+4) = (x-7)/(2x-4)
x^2 - 15x = 0 => x=17 km.
So one round trip = 2*17 = 34 km.
as given each bus make 5 round trips in a day.

so total distance cover by both buses = 34 * 2 *5 = 340 km.
Cost of travelling per bus = 340 * 20 = Rs. 6800.

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26. A man sets out to cycle from Delhi to Rohtak and at the same time another man starts from Rohtak to cycle to cycle to Delhi. After passing each other they completed their journey in (10/3) hours and (16/3) hours respectively.At what rate does the second man cycle if the first cycle at 8 kmph?

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Explanation:

A's Speed:B's Speed=rootof(b):rootof(a)
=>8:x=rootof(10/3):rootof(16/3)
On solving we get,
=> x=2*rootof(10)
=> x=2*3.16
=> x=6.32 kmph.

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27. The distance between 2 persons is 800m. If they start moving towards each other simultaneously at 10m/s and 15m/s, in how much time do they meet?

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Explanation:

Total speed of both person = 10 + 15 = 25 m/s

Distance between both persons = 800m
so they meet after 800/25 = 32 sec.

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28. A scooterist covers a certain distance at 36 kmph. How many meters does he cover in 2 min?

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Explanation:

Speed = 36 kmph = 36 * 5/18 = 10mps
So, Distance covered in 2 min = (10 * 2 * 60)m = 1200 meters.

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29. The diameter of the driving wheel of a bus is 140cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?

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Explanation:

Distance to be covered in 1 min=(66*1000)/60 m=1100m
Circumference of the wheel =(2*22/7*0.70)m=4.4m.
So, Number of revolutions per min=1100/4.4=250.

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30. By walking at 3/4th of his usual speed, a man reaches office 20 minutes later than usual. What is his usual time?

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