Time and Distance Problems with Detailed Solutions

Ques 1.

It is 200 miles from Jaipur to Coimbatore . If a bus takes 2 hours to travel the first 75 miles.How long must the train  take to travel the final 125 miles in order to have an average of 50 miles per hour for the entire trip ?

(a) 60 minutes
(b) 94 minutes
(c) 120 minutes
(d) 110 minutes

Ques 2.

Vijay  rows 3 km per hour in still water. if the river is running at 1 km per hour , it takes him    45    minutes to row  to a place and back .How far is the place ?
(a) 2 km
(b) 1.5
(c) 1 km
(d) 2.5 km

Ques 3.

Ram starts walking . He walked 2 km in the first hour . Then he walked two-thirds of the distance of the previous hour in each next hour . If he walked continuously then how long could he walk maximum ?
(a)  60 km
(b)  7 km
(c)  12 km
(d)  8 km

Ques 4.

Ravi leaves home for stadium which is 12 km from his house .After the stadium, he goes to his club which is 7 km from his stadium . If his house, stadium and club all fail in a time, then what is the minimum distance he has to travel to get back home ?
(a) 19 km
(b) 7 km
(c) 5 km
(d) 12 km

Ques 5.

I walk a certain distance and ride back talking a total time of 37 minutes . i could walk both ways in 55 minutes . How long would it take me to ride both ways.?
(a) 9.5 minutes
(b) 19 minutes
(c) 18 minutes
(d) 20 minutes

Ques 6.

Sudhir cycles with a speed of 10 km/h and reaches his bank  at 1 pm. however, when he cycles with a speed of 15 km/h , he reaches his bank at 11 am. At what speed should he cycle, so that he reaches his bank at 12 noon ?
(a) 12.5 km/h
(b) 12 km/g\h
(c) 13 km/h
(d) 13.5 km/h

Ques 7.

A railway engine moves with the speed of 42 km/h. The reduction in speed varies as the square root of the number of compartments attached to it. The speed is 24 km when 9 compartments are attached. What is the maximum number of compartments that the engine can pull
(a) 47
(b) 48
(c) 49
(d) 42

Ques 8.

Three runners A ,B  and  C run a race , with runner A finishing 12 meters ahead of runners  B and 18 meters ahead of runners C , while  runners B finishes 8 meters ahead of C. Each  runners travels  the entire distance at constant speed . What was the length of the race ?
(a) 36 meters 
(b) 48 meters 
(c) 60 meters 
(d) 72 meters

Ques 9.

If a man cycles at 10 km/hr, then he arrives at a certain place place at 1 p.m .If he cycles at 15 km/hr, he will arrive at the same place at 11 a.am  At what speed must he cycles to get there at noon ?
(a) 11 km/hr
(b) 12 km/hr
(c) 13 km/hr
(d) 14 km/hr

Ques 10.

 Two boats, traveling at 5 and 10 km per hour, head directly towords each other . They begin at a  distance 20 km from each other. How far apart are they (in kms ) one minute before they collide?

solutions:

Ans.1 (c)


Ans.2

 (c) Suppose distance is x km
  ⇒speed in downstream = ( 3 + 1) km/hr = 4 km/hr
  ⇒speed in upstream = ( 3 + 1) km/hr = 2 km/hr

  According to question
⇒ Time-taken by vijay  for downstream + time- taken for upstream = 

Ans.3

Required distance =



Ans.4

(d)  House 5 km   house  7 km   stadium


Ans.5

(a) Time taken in walking a certain distance from x to y =



Time-taken in riding the same distance =


Ans.6

Let t h be the time taken by the sudhir to reach his bank at the speed of 15 km/hr Then , time taken to reach the bank at the speed of 10 km/hr = (t + 2) h. Now.

 speed required to reach the bank at 12 noon ( i.e. in 5 h ) = distance / time

Thus, speed =

Ans.7

      Let r = reduction in speed and w = number of wagons
      Given that  r a /w
      r'  =  42 - 24  = 18 ;  w'  = 9
      Now let us find out how many wagons will be required so that the train stops . For tht let's take           the speed as 0.
      For this to happen the reduction has to be 42.
     With 49 wagons the train will stop.
     Thus we subtract one wagon so that the train will just move.
     Hence the answer is 48.

Ans.8

(b) Let l be length in meters pf the race which A finishes in t seconds.
speed of A = speed of B=




  speed of C=



 Time taken by B to finish the race =



In this time, C covers ( L- 8 ) m,



  Ans.9





=> 10 x = 15 x - 30 or 5 x = 30 or x = 6 hrs and d = 60 km


=> To reach at noon, he cycles for 5 hrs


=> Thus , he cycles at speed =



Ans.10

(c) Relatives velocity of the boats = 15 km/hour =


Therefore, they cover 1/4 km in the last one minute before collision.




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