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Important Formulae

1. Speed, Time and Distance Relation:
Speed = Distance/Time
Time = Distance/Speed
Distance = (Speed x Time)

2. km/hr to m/sec conversion:
X km/hr = X x 5/18 m/sec.

3. m/sec to km/hr conversion:
X m/sec = X x 18/5 km/hr.

4. If the ratio of the speeds of A and B is a : b, then the ratio of the
the times taken by then to cover the same distance is 1/a : 1/b or b : a.

5. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then, the average speed during the whole journey is 2xy/x+y km/hr.

Practice Questions

1.

A man leaves P and reaches Q in 3 hours at an average speed of 60 kmph. What is the distance from P to Q?
A.240 kmB.150 km
C.300 kmD.180 km

Report! Answer!

Answer is: D

The distance between P and Q = 3 x 60 = 180 km

2.

A left P for Q at 9:00 am and B left P for Q at 10:00 am. If the speeds of A and B are 60 kmph and 80 kmph respectively, at what time do they meet, given that P and Q are 1000 km apart?
A.12:00 pmB.1:00 pm
C.2:00 pmD.12:30 pm

Report! Answer!

Answer is: B

From 9:00 am to 10:00 am , A travels for 1 hour i.e. 60 km.
At 10:00 am B and A are separated by 60 km.
The relative speed of B with respect to A = 80 - 60 = 20 kmph.
(since, A and B are travelling in the same direction)
The time taken by B to meet A = 60/20 = 3 hours.
At 10:00 am + 3 hours = 1:00 pm, B meets A.

3.

A person travelled from hyderabad to chennai at an average speed of 30 kmph and then came bvack to hyderabad at an average speed of 90 kmph along the same route. What is the average speed for the entire journey?
A.75 kmphB.60 kmph
C.45 kmphD.cannot be determined

Report! Answer!

Answer is: C

Let the distance be 'd'
Total distance travelled = 2d
Total time taken = (d/30) + (d/90)
Average speed = 2d/{(d/30) + (d/90)} = (2 x 30 x 90)/(30 + 90) = 45 kmph.

4.

P started running towards north at 6:00 am and Q started running towards north at 8:00 am. At what time do they meet, if their speeds are In the ratio 3 : 5?
A.11:00 amB.10:00 am
C.12:00 amD.cannot be determined

Report! Answer!

Answer is: D

If Q starts from the same point from which P started, then the distance of separation between them is the distance travelled by P in 2 hours, (because 8:00 am - 6:00 am = 2 hours).
The information about the starting points of P and Q is not available. Hence, the question cannot be answered.

5.

If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
A.50 kmB.56 km
C.70 kmD.80 km

Report! Answer!

Answer is: A

Let the actual distance travelled be X km.
Then, X/10 = (X + 20)/14
14X = 10X + 200
4X = 200
X = 50 km

6.

A travelled for 3 hours at a speed of 60 kmph, and then for 4 hours at a speed of 95 kmph. What is the average speed of the journey?
A.155 kmphB.77.5 kmph
C.80 kmphD.100 kmph

Report! Answer!

Answer is: C

Total distance travelled by A = 3 x 60 + 4 x 95 = 560 km.
Total time taken = 3 + 4 = 7 hours.
Average speed = 560/7 = 80 kmph.

7.

Ganesh and Suresh are running along a circular track of length 300 m. If the speed of Ganesh and Suresh are 6 m/sec and 12 m/sec respectively. How many rounds more than Ganesh will Suresh complete in 1 hour?
A.36B.108
C.144D.72

Report! Answer!

Answer is: D

Difference in speeds of Suresh and Ganesh is = 12 - 6 = 6 m/sec.
The difference in number of rounds made = Number of rounds made at 6 m/sec.
i.e. (6 x 3600)/300 = 72.

8.

Dheeraj travelled for 2 hours at an average speed of 48 kmph and travelled for another 2 hours at an average speed of 52 kmph . What is the average speed? (in kmph)
A.49 kmB.50 km
C.51 kmD.52 km

Report! Answer!

Answer is: B

As the duration of journey at different speeds is constant, the average speed of the journey is average of the speeds.
i.e. (48 + 52)/2 = 50 kmph.

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