**IMPORTANT FACTS AND FORMULAE**

**1.** Speed = [Distance/Time],

Time=[Distance/Speed],

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

**Hint**:

Speed = [1200/(5 x 60)] m/sec = 4 m/sec.

Converting m/sec to km/hr

= (4 x 18/5) km/hr

=14.4 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**

**Hint** :

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

**Hint** :

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

**Hint** :

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.