1. The wheel of an engine of 300 cm in circumference makes 10 revolutions in 6 seconds. What is the speed of the wheel (in km/h)?

a) 18

b) 20

c) 27

d) 36

Explanation: Circumference = One revolution

Distance covered in 10 revolutions = 300 * 10 = 3000 cm = 30 m

30 meters are covered in 6 seconds.

Speed of the wheel = $$\frac{{30}}{{\text{6}}}$$ = 5 m/s

5 m/s = $$\frac{{5 \times 18}}{5}$$ = 18 km/h. [ To convert m/s to km/h, we use to multiply by factor $$\frac{{18}}{5}$$ ]

2. A thief sees a jeep at a distance of 250 m, coming towards him at 36 km/h. Thief takes 5 seconds to realize that there is nothing but the police is approaching him by the jeep and start running away from police at 54 km/h. But police realise after 10 second, when the thief starts running away, that he is actually a thief and gives chase at 72 km/h. How long after thief saw police did catchup with him and what is the distance police had travel to do so?

a) 50 s, 1000 m

b) 65 s, 1150 m

c) 65 s, 1300 m

d) 45 s, 1050 m

Explanation: Initial speed of the police = 10 m/s

Increased speed of the Police = 20 m/s

Speed of the thief = 15 m/s

Initial difference between speed of thief and police = 250 m

After 5 seconds difference between thief and police = 200 + (5 × 10) = 250 m

The time required by police to catch the thief = $$\frac{{250}}{5}$$ = 50 s

Total time = 50 + 15 = 65 s

Total distance = 1000 + (15 × 10) = 1150 m

3. A person X starts from Lucknow and another person Y starts from Kanpur to meet each other. Speed of X is 25 km/h, while Y is 35 km/h. If the distance between Lucknow and Kanpur be 120 km and both X and Y start their journey at the same time, when they will meet ?

a) 1 hours later

b) 2 hours later

c) $$\frac{1}{2}$$ hours later

d) 3 hours later

Explanation: Lucknow(X →)_____120 km _____(← Y)Kanpur

Relative speed = (25+35) = 60 km/h

Time taken to complete 120 km

= $$\frac{{120}}{{60}}$$ = 2 h

They will meet 2 hours later.

4. Two persons A and B started from two different places towards each other. If the ratio of their speed be 3 : 5, then what is the ratio of distance covered by A and B respectively till the point of meeting?

a) 1 : 2

b) 3 : 4

c) 3 : 5

d) 5 : 3

Explanation: When time is constant the distance covered by A and B will be in the ratio of their speeds. i.e. ratio of distance is 3 : 5 as time is constant.

5. The ratio of speeds of A and B is 2 : 3 and therefore A takes 20 minutes more time than B. What is the ratio of time taken by A and B?

a) 2 : 3

b) 2 : 5

c) 3 : 2

d) 3 : 5

Explanation: When distance is constant then Speed is inversely proportional to time.

ST = D

When distance constant,

S ∝ $$\frac{1}{{\text{T}}}$$

Ratio of time taken by A and B = 3 : 2

6. From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hour. If A traveled with $$\frac{2}{3}$$ of his speed and B traveled with double of his speed, they would have met after 5 hours. The speed of A is:

a) 4 km/h

b) 6 km/h

c) 10 km/h

d) 12 km/h

Explanation: A →_______60Km_________← B

Let the speed of A = x kmph and that of B = y kmph

x × 6 + y × 6 = 60

x + y = 10 --------- (i)

$$\left( {\frac{{2{\text{x}}}}{3} \times 5} \right) + \left( {2{\text{y}} \times 5} \right) = 60$$

10x + 30y = 180

x + 3y = 18 ---------- (ii)

From equation (i) × 3 - (ii)

3x + 3y - x - 3y = 30 - 18

2x = 12

x = 6 kmph

7. A, B and C start together from the same place to walk round a circular path of length 12km. A walks at the rate of 4 km/h, B 3 km/h and C $$\frac{3}{2}$$ km/h. They will meet together at the starting place at the end of:

a) 10 hours

b) 12 hours

c) 15 hours

d) 24 hours

Explanation: Time taken to complete the revolution:

A → $$\frac{{12}}{{4}}$$ = 3 hours

B → $$\frac{{12}}{{3}}$$ = 4 hours

C → 12 × $$\frac{{2}}{{3}}$$ = 8 hours

Required time

= LCM of 3, 4, 8

= 24 hours

8. Ravi and Ajay start simultaneously from a place A towards B 60 km apart. Ravi's speed is 4km/h less than that of Ajay. Ajay, after reaching B, turns back and meets Ravi at a places 12 km away from B. Ravi's speed is:

a) 12 km/h

b) 10 km/h

c) 8 km/h

d) 6 km/h

Explanation:

Ajay → (x + 4) kmph.

A ________ 60 km _________ B

Ravi → x kmph.

Let the speed of Ravi be x kmph;

Hence, Ajay's speed = (x + 4) kmph;

Distance covered by Ajay = 60 + 12 = 72 km;

Distance covered by Ravi = 60 - 12 = 48 km.

$$\eqalign{ & \frac{{72}}{{x + 4}} = \frac{{48}}{x} \cr & \frac{3}{{x + 4}} = \frac{2}{x} \cr & 3x = 2x + 8 \cr & x = 8\,{\text{kmph}} \cr} $$

9. The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. Time in which A reach the destination?

a) $$1\frac{1}{3}$$ hours

b) 2 hours

c) $$2\frac{2}{3}$$ hours

d) $$1\frac{2}{3}$$ hours

Explanation: Ratio of speed = 3 : 4

Ratio of time taken = 4 : 3 (As Speed ∝ $$\frac{1}{{{\text{Time}}}},$$ When distance remains constant.)

Let time taken by A and B be 4x and 3x hour respectively.

4x - 3x = $$\frac{{20}}{{60}}$$

x = $$\frac{{1}}{{3}}$$

Hence, time taken by A = 4x

hours = 4 × $$\frac{1}{3}$$ = $$1\frac{1}{3}$$ hours.

10. A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. His average speed is

a) 9 km/h

b) 4.5 km

c) 4 km/h

d) 3 km/h

Explanation:

$$\eqalign{ & {\text{Average}}\,{\text{speed}} \cr & = \frac{{2xy}}{{ {x + y} }} \cr & = \frac{{2 \times 6 \times 3}}{{ {6 + 3} }} \cr & = \frac{{36}}{9} \cr & = 4\,{\text{kmph}} \cr} $$