Sample Material of Online Coaching For SSC CGL (Tier - 2) - Time and Distance
Sample Material SSC CGL TIER-2 Online Coaching
Numerical Aptitude (Chapter: Time and Distance)
Relation between Time, Speed and Distance
Distance covered, time and speed are related by
Time = Distance ...(i) Speed
Speed = Distance ...(ii) Time
Distance = Speed × Time ...(iii)
- Distance is measured in metres, kilometres and miles.
- Time in hours, minutes and seconds.
- Speed in km/h, miles/h and m/s.
1. To convert speed of an object from km/h to m/s multiply the speed by 5 . 18
2. To convert speed of an object from m/s to km/h, multiply the speed by 18 . 5
Average Speed
It is the ratio of total distance covered to total time of journey.
Therefore Average speed = Total distance covered Total time of journey
General Rules for Solving Time & Distance Problems
Rule 1
If a certain distance is covered with a speed of ‘x’ km/h and another equal distance with a speed of ‘y’ km/h, then the average speed for the whole journey is the harmonic mean of the two speeds.
Average speed =
Rule 2
If three equal distances are covered by three different speeds x, y and z km/h, then average speed for the whole journey is given by
Average speed =
Rule 3
If a certain distance is covered with a speed of ‘x’ km/h and another distance with a speed of ‘y’ km/h but time interval for both journeys being same, then average speed for the whole journey is given by
Average Speed = (x+y)km/h 2
Rule 4
If a certain distance is covered with a speed of x, y and z km/h, but time inverval for the three journey being equal, then average speed is given by
Average speed = (x+y+z)km/h 3
Rule 5
If the ratio of speeds A and B is x : y, then the ratio of times taken by them to cover the same distance is 1 : 1 x y
Relative Speed
- If two bodies are moving in the same direction at x km/h and y km/h, where (x > y), then their relative speed is given by (x – y) km/h.
- If two bodies are moving in opposite direction at x km/h and y km/h, then their relative speed is given by (x + y) km/h.
General Rules for Solving Train Problems
Rule 1 Train Vs Stationary Object of no Length
Time taken by a train of length ‘l’ metre to pass a stationary object such as a pole, standing man or a building is equal to the time taken by the train to cover l metre.
Speed of the train = Length of the train Time taken to cross the stationary object
Rule 2 Train Vs Stationary Object of Certain Length
Time taken by a train of length ‘l’ metre to pass a stationary object of length ‘a’ metre such as another standing train, bridge or railway platform is equal to the time taken by the train to cover (l + a) metre.
Speed of the train = Length of the train + Length of the stationary object Time taken to cross the stationary object
Rule 3 Train Vs Moving Object of no Length
Time taken by the train of length ‘l’ metre to pass a man moving is equal to the time taken by the train to cover l metre
(i) When the train and man move in the same direction with speeds of x m/s and y m/s. Then,
(x – y) = Length of the train Time taken to cross each other
(ii) When the train and man move in opposite directions with speeds of x m/s and y m/s. Then,
(x + y) = Length of the train Time taken to cross each other
Rule 4 Train Vs Moving Object of Certain Length
Time taken by the train of length ‘l’ metre to pass a moving object of length ‘a’ metre such as another moving train is equal to the time taken by the train to cover (l + a) metre.
(i) When the two trains move in the same direction with speeds of x m/s and y m/s, (x > y), then
(x – y) = Length of the train + Length of train two
Time taken to cross each other
(ii) When the two trains move in opposite directions with speeds of x m/s and y m/s. Then,
(x + y) = Length of the train + Length of train two
Time taken to cross each other
:: Home Assignment for Practice ::
1.The average speed of a train in the onward journey is 25% more than that in the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and for journey is 17 hours, covering a distance of 800 km. The speed of the train in the onward journey is:
(a) 50 km/hr
(b) 53 km/hr
(c) 52 km/hr
(d) 56.25 km/hr
2. I started on my bicycle at 7 a.m. to reach a certain place. After going a
certain distance, my bicycle went out of order. Consequently, I rested for 35
minutes and came back to my house walking all the way. I reached my house at 1
p.m. If my cycling speed is 10 kmph and my walking speed is 1 kmph, then on my
bicycle I covered a distance of:
3. A, B and C are on a trip by a car. A drives during the first hour at an
average speed of 50 km/hr. B drives during the next 2 hours at an average speed
of 48 km/hr. C drives for the next 3 hours at an average speed of 52 km/hr. They
reached their destination after exactly 6 hours. Their mean speed was:
(a) 50 km/hr
(b) km/hr
(c) 51 km/hr
(d) 52 km/hr
4. A man on tour travels first 160 km at 64 km/hr and the next 160 kin at 80 km/hr. The average speed for the first 320 km of the tour is:
(a) 35.55 km/hr
(b) 38 km/hr
(c) 71.11 km/hr
(d) 75 km/hr
5. A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately :
(a) 10.4 km/hr
(b) 10.8 km/hr
(c) 12 km/hr
(d) 14 km/hr