Time and Distance Problems and Solutions

• 15. A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 7:30 am. They shall first cross each other at ?

  1. 7:15 am
  2. 7:30 am
  3. 7: 42 am
  4. 7:50 am

  Answer :

  Option C

  Explanation:

  Relative speed between two = 6-1 = 5 round per hour
  
  They will cross when one round will complete with relative speed,
  which is 1/5 hour = 12 mins.
  
  So 7:30 + 12 mins = 7:42

• 16. A train traveled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point.

  1. 6 hours 24 mins
  2. 6 hours 21 mins
  3. 6 hours 18 mins
  4. 6 hours 15 mins

  Answer :

  Option B

  Explanation:

  Time taken to cover 600 km = 6 hours [because train speed is 100 km/hr]
  
  Number of stops =
  egin{aligned}
  frac{600}{75} - 1 = 7 \
  ext{Total time on stops =}7*3 = 21 mins
  
  end{aligned}
  Total time taken by train = 6 hours 21 mins
  

• 17. 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?

  1. 11:9
  2. 13:9
  3. 17:9
  4. 21:9

  Answer :

  Option A

  Explanation:

  We know total distance is 200 Km
  If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110+90=200km]
  So ratio of their speed = 110:90 = 11:9

• 18. A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.

  1. 50 km/hr
  2. 60 km/hr
  3. 65 km/hr
  4. 70 km/hr

  Answer :

  Option B

  Explanation:

  We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.
  Lets solve it.
  
  Time = 50/60 hr = 5/6 hr
  Speed = 48 mph
  Distance = S*T = 48 * 5/6 = 40 km
  
  New time will be 40 minutes so,
  Time = 40/60 hr = 2/3 hr
  Now we know,
  Speed = Distance/Time
  New speed = 40*3/2 kmph = 60kmph

• 19. 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 ?

  1. 8 minutes
  2. 10 mintues
  3. 12 minutes
  4. 14 minutes
  5. Only argument I is strong
  6. Only argument II is strong
  7. Either I or II is strong
  8. Neither I nor II is strong
  9. Both I and II are strong

  Answer :

  Option F

  Explanation:

  Due to stoppages, it covers 9 km less.
  
  Time taken to cover 9 km = (9/54) hour
  = (1/6)*60 minutes
  = 10 minutes

• 20. A person crosses a 600 meter long street in 5 minutes. What is the speed in Km/hr

  1. 6.2 km/hr
  2. 7.2 km/hr
  3. 8.2 km/hr
  4. 9.2 km/hr
  5. Only conclusion I follows
  6. Only conclusion II follows
  7. Either I or II follows
  8. Neither I nor II follows
  9. Both I and II follow

  Answer :

  Option

  Explanation:

  Two things to give attention on this question.
  First time is in minutes, we need to change it to seconds to get speed in m/sec, then we need to get the final answer in km/hr.
  So lets solve this.
  
  \begin{aligned}
  Speed = \frac{Distance}{Time} \\
  Distance = 650 meter \\
  Time = \text{5 minutes} = 300 sec \\
  Speed = \frac{600}{300} = 2 m/sec \\
  
  => 2*\frac{18}{5} km/hr = 7.2 km/hr
  \end{aligned}

• 21. 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?

  1. 15 hours
  2. 16 hours
  3. 17 hours
  4. 18 hours

  Answer :

  Option C

  Explanation:

  In this type of questions we need to get the relative speed between them,
  The relative speed of the boys = 5.5kmph – 5kmph
  = 0.5 kmph
  
  Distance between them is 8.5 km
  Time = Distance/Speed
  Time= 8.5km / 0.5 kmph = 17 hrs