IMPORTANT FACTS AND FORMULAE
1. Speed = [Distance/Time],
Distance = (Speed×Time)
2. x km/hr = [x×5/18] m/sec.
3. If the ratio of the speeds of A and B is a:b, then the ratio of the times taken by them to cover the same distance is 1/a : 1/b or b:a.
4. x m/sec = [x×18/5] km/hr.
5. if a Boy 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.
6. Speed and time are inversely proportional (when distance is constant) ⇒Speed ∝ 1/Time (when distance is constant).
Objective Type Questions & Answers
1. A person crosses a 1200 m long street in 5 minutes. What is his speed in km per hour?
A. 8.6 B. 14.4
C. 12.4 D. 20
Answer : Option B
Speed = [1200/(5 x 60)] m/sec = 4 m/sec.
Converting m/sec to km/hr
= (4 x 18/5) km/hr
2. An aeroplane covers a certain distance at a speed of 260 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:
A. 400 kmph B. 560 kmph
C. 800 kmph D. 780 kmph
Answer : Option D
Distance = (260 x 5) = 1300 km.
Speed = Distance/Time
Speed = 1300/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = (1300 x 3/5) km/hr = 780 km/hr.
3. If a person walks at 15 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
A. 40 km B. 46 km
C. 50 km D. 60 km
Answer : Option A
Let the actual distance travelled be x km.
Then, x/10 = (x + 20)/15
15x = 10x + 200
5x = 200
x = 40 km.
4. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
A. 100 kmph B. 110 kmph
C. 120 kmph D. 130 kmph
Answer : Option C
Let speed of the car be x kmph.
Then, speed of the train = (150/100) x = (3/2) x kmph.
[(75/x) – 75/(3/2)x] = 125/(60×10)
[(75/x) – (50/x)] = 5/24
x = (25 x24)/5 = 120 kmph.