Time and Distance Quiz Test

Important Formulas :

i) Speed = Distance/Time
ii) Time = Distance/speed
iii) Distance = speed*time
iv) 1km/hr = 5/18 m/s
v) 1 m/s = 18/5 Km/hr
vi) If  the  ratio  of  the  speed  of  A  and  B  is  a:b,then the  ratio  of  the  time taken by them to cover the same distance is 1/a : 1/b or b:a
vii)  suppose  a  man  covers  a  distance  at  x  kmph  and  an  equal  distance  at  y kmph.then the average speed during the whole journey is (2xy/x+y) kmph
viii) An object that moves at a constant rate is said to be in uniform motion. The formula d = rt gives  the  relationship  between  distance d,  rate r,  and  time t. Uniform  motion  problems  may  involve  objects  going  the  same  direction, opposite directions, or round trips.

Questions :

1.) Walking at the rate of 4kmph a man cover certain distance in 2hr 45 min. Running at a
speed of 16.5 kmph the man will cover the same distance in.
A. 12 min B. 25 min C. 40min D. 60 min
Answer: Option C
Explanation: Distance = Speed * time
4*11/4 = 11km
New Speed = 16.5 kmph
Therefore time = D/S = 11/16.5 = 40min

 

2.) A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The
speed at which the train must run to reduce the time of journey to 40min will be.
A. 45 min B. 60 min C. 75 min D. None of these
Answer: Option B
Explanation: Time = 50/60 hr = 5/6hr
Speed = 48mph
distance = S*T = 48 * 5/6 = 40km
time = 40/60hr = 2/3hr
New speed = 40* 3/2 kmph = 60kmph

 

3.) Two  boys  starting  from  the  same  place  walk  at  a  rate  of  5kmph  and  5.5kmph
respectively.  What  time  will  they  take  to  be  8.5km  apart,  if  they  walk  in  the  same
direction?
A. 17 hrs B. 25 hrs C. 31 hrs D. 45 hrs
Answer: Option A
Explanation:
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs

 

4.) Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45
kmph. For how many minutes does the bus stop per hour?
A. 4 B. 6 C. 8 D. None of these
Answer: Option D
Explanation:
Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54 x 60) min = 10 min.

 

5.) 2 trains starting at the same time from 2 stations 200km apart and going in opposite
direction cross each other at a distance of 110km from one of the stations. What is the
ratio of their speeds?
A. 7:3 B. 11:9 C. 18:4 D. None of these
Answer: Option B
Explanation:
In same time, they cover 110km & 90 km respectively
so ratio of their speed =110: 90 = 11: 9

 

6.) In  covering  a  distance  of  30  km,  Sachin  takes  2  hours  more  than  Rohit.  If  Sachin
doubles his speed, then he would take 1 hour less than Rohit. Sachin speed is:
A. 5 kmph B. 16 kmph C. 21 kmph D. None of these
Answer: Option A
Explanation:
Let Sachin’s speed be X km/hr.
Then, 30/x - 30/2x = 3
6x = 30
x = 5 km/hr.

 

7.) A train 140m long running at 60kmph. In how much time will it pass a platform 260m
long?
A. 5 kmph B. 16 kmph C. 21 kmph D. None of these
Answer: Option A
Explanation:
Distance travelled = 140 + 260m = 400m,
Speed = 60 * 5/8 = 50/3m
Time = 400 * 3/50 = 24 Seconds

 

8.) The ratio between the speeds of two trains is 7: 8. If the second train runs 440 kms in 4
hours, then the speed of the first train is:
A. 47.4 km/hr B. 57.19 km/hr C. 68.13 km/hr D. None of these
Answer: Option D
Explanation:
Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = (440/4) = 110
x = (110/8) = 13.75
Speed of first train = (7 x 13.75) km/hr = 96.25 km/hr.

 

9.) Sachin can cover a distance in 1hr 24min by covering 2/3 of the distance at 4 kmph
and the rest at 5kmph.the total distance is?
A. 5km B. 6km C. 7km D. 8km
Answer: Option D
Explanation:
Distance = 2/3S
distance=1-2/3S=1/3S
21/15 hr=2/3 S/4 + 1/3s /5
84=14/3S * 3
S= 6km

 

10.) A person walks at 5kmph for 6hr and at 4kmph for 12hr.The average speed is.
A. 4 1/3 B. 7 2/3 C. 9 ½ km D. 8km
Answer: Option D
Explanation:
Avg speed = total distance/total time
= 5*6 + 4*12 / 18
=4 1/3 mph