Aptitude Questions With Answers for Time & Distance Problems

1) 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.?

1. Solution::

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

2) Vikas 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?

2. Solution::

Let total distance be S

Total time=1hr24min

A to T :  speed=4kmph

Distance =2/3S

T to S :: speed=5km

Distance =1-2/3S=1/3S

21/15 hr=2/3 S/4 + 1/3s /5

84=14/3S*3

S=84*3/14*3= 6km

3) Walking at ¾ of his usual speed, a man is late by 2 ½ hr. the usual time is.?

3. Solution:

Usual speed = S

Usual time = T

Distance = D

New Speed is ¾ S

New time is 4/3 T

4/3 T – T = 5/2

T=15/2 = 7 ½

4) A man covers a distance on scooter .had he moved 3kmph faster he would have taken 40 min less. If he had moved 2kmph slower he would have taken 40min more the distance is.?

  4. Solution:  

Let distance = x m

Usual rate = y kmph

x/y – x/y+3 = 40/60 hr

2y(y+3) = 9x ————–1

x/y-2 – x/y = 40/60 hr y(y-2) = 3x —————–2

Divide 1 & 2 equations by solving we get x = 40

5) Excluding stoppages, the speed of the bus is 54kmph and including stoppages, it is 45kmph.for how many min does the bus stop per hr.?

5. Solution::

Due to stoppages, it covers 9km less. time taken to cover 9 km is [9/54 *60] min = 10min

6) Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively.wht time will they take to be 8.5km apart, if they walk in the same direction?

6. Solution::

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

7)2 trains starting at the same time from 2 stations 200km apart and going in opposite direction cross each other ata distance of 110km from one of the stations. What is the ratio of their speeds.

7. Solution::

In same time, they cover 110km & 90 km respectively so ratio of their speed =110:90 = 11:9

8) Two trains start from A & B and travel towards each other at speed of 50kmph and 60kmph resp. At the time of the meeting the second train has traveled 120km more than the first the distance between them?

8. Solution:

Let the distance traveled by the first train be x km

then distance covered by the second train is x + 120km

x/50 = x+120 / 60

x= 600

so the distance between A & B is x + x + 120 = 1320 km

9) A thief steals a ca r at 2.30pm and drives it at 60kmph.the theft is discovered at 3pm and the owner sets off in another car at 75kmph when will he overtake the thief?

9. Solution::

Let the thief is overtaken x hrs after 2.30pm

Distance covered by the thief in x hrs = distance covered by

the owner in x-1/2 hr

60x = 75 ( x- ½)

x= 5/2 hr

thief is overtaken at 2.30 pm + 2 ½ hr = 5 pm

10) In covering distance, the speed of A & B are in the ratio of 3:4.A takes 30min more than B to reach the destion.The time taken by A to reach the destination is?

10. Solution::

Ratio of speed = 3:4

Ratio of time = 4:3

let A takes 4x hrs,B takes 3x hrs

then 4x-3x = 30/60 hr

x = ½ hr

Time taken by A to reach the destination is 4x = 4 * ½ = 2 hr

Submitted by Subbaiah