416. A bus covers four successive 3 km stretches at speed of 10 km/hr, 20 km/hr, 30 km/hr and 60 km/hr respectively. Its average speed over this distance is

1. 1. 30 km/hr

   
   
   

   2. 25 km/hr

   
   
   

   3. 20 km/hr

   
   
   

   4. 10 km/hr

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Average speed =	Total distance
   	Time taken

   
   

   =	12
   	3	+	3	+	3	+	3
   	10		20		30		60

   
   

   =	12
   	3		6 + 3 + 2 + 1
   			60

   
   

   =	12 × 60	= 20 kmph
   	3 × 12

   Correct Option: C

   Average speed =	Total distance
   	Time taken

   
   

   =	12
   	3	+	3	+	3	+	3
   	10		20		30		60

   
   

   =	12
   	3		6 + 3 + 2 + 1
   			60

   
   

   =	12 × 60	= 20 kmph
   	3 × 12

---

417. A bus moving at a speed of 45 km/hr overtakes a truck 150 metres ahead going in the same direction in 30 seconds. The speed of the truck is

1. 1. 27 km/hr

   
   
   

   2. 24 km/hr

   
   
   

   3. 25 km/hr

   
   
   

   4. 28 km/hr

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the speed of the truck be x kmph
   Relative speed of the bus = (45 - x) kmph
   

   ∴   Time =	Distance
   	Relative speed

   
   

   ⇒	30
   	60 × 60

   
   

   =	150
   	1000
   	(45 − x)

   
   

   ⇒	1	=	15
   	120		100(45 − x)

   
   

   ⇒	1	=	3	⇒ (45 − x) = 18
   	6		(45 − x)

   
   ⇒  x = 45 – 18 = 27 kmph

   Correct Option: A

   Let the speed of the truck be x kmph
   Relative speed of the bus = (45 - x) kmph
   

   ∴   Time =	Distance
   	Relative speed

   
   

   ⇒	30
   	60 × 60

   
   

   =	150
   	1000
   	(45 − x)

   
   

   ⇒	1	=	15
   	120		100(45 − x)

   
   

   ⇒	1	=	3	⇒ (45 − x) = 18
   	6		(45 − x)

   
   ⇒  x = 45 – 18 = 27 kmph

---

---

418. The speeds of three cars are in the ratio of 1 : 3 : 5. The ratio among the time taken by these cars to travel the same distance is

1. 1. 3 : 5 : 15

   
   
   

   2. 15 : 3 : 5

   
   
   

   3. 15 : 5 : 3

   
   
   

   4. 5 : 3 : 1

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Speed ∝	1
   	Time

   
   

   ∴   Required ratio of time = 1 :	1	:	1
   	3		5

   
   

   = 15 :	1	× 15 :	1	× 15
   	3		5

   
   = 15 : 5 : 3

   Correct Option: C

   Speed ∝	1
   	Time

   
   

   ∴   Required ratio of time = 1 :	1	:	1
   	3		5

   
   

   = 15 :	1	× 15 :	1	× 15
   	3		5

   
   = 15 : 5 : 3

---

419. A thief is noticed by a policeman from a distance of 200m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km./hr and 11 km./hr respectively. What is the distance between them after 6 minutes ?

1. 1. 100 m

   
   
   

   2. 190 m

   
   
   

   3. 200 m

   
   
   

   4. 150 m

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Relative speed of police
   = 11 – 10 = 1 kmph
   

   =	5	m/sec
   	18

   
   

   ∴  Distance decreased in 6 minutes =	5	× 6 × 60
   	18

   
   = 100 m
   ∴  Distance remained between them = 200–100 = 100 m

   Correct Option: A

   Relative speed of police
   = 11 – 10 = 1 kmph
   

   =	5	m/sec
   	18

   
   

   ∴  Distance decreased in 6 minutes =	5	× 6 × 60
   	18

   
   = 100 m
   ∴  Distance remained between them = 200–100 = 100 m

---

---

420. A moving train, 66 metres long, overtakes another train of 88 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 30 km/hr, at what speed is the first train moving ?

1. 1. 85 km/hr.

   
   
   

   2. 50 km/hr.

   
   
   

   3. 55 km/hr.

   
   
   

   4. 25 km/hr.

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Suppose the speed of first train be x kmph
   Speed of second train = 30 kmph
   

   =	3 × 1000	= 500 m per min.
   	60

   
   ∴  According to question
   

   Total Distance

   Relative speed

   
   

   =	(66 + 88)	= 0.168
   	x − 500

   
   

   ⇒	154	= 0.168
   	x − 500

   
   ⇒  0.168x – 84 = 154
   ⇒  0.168x = 238
   

   ⇒  x =	238
   	0.168

   
   

   =		238 × 1000		m per minute
   		168

   
   

   =	238 × 1000	×	3	kmph
   	168		50

   
   = 85 kmph

   Correct Option: A

   Suppose the speed of first train be x kmph
   Speed of second train = 30 kmph
   

   =	3 × 1000	= 500 m per min.
   	60

   
   ∴  According to question
   

   Total Distance

   Relative speed

   
   

   =	(66 + 88)	= 0.168
   	x − 500

   
   

   ⇒	154	= 0.168
   	x − 500

   
   ⇒  0.168x – 84 = 154
   ⇒  0.168x = 238
   

   ⇒  x =	238
   	0.168

   
   

   =		238 × 1000		m per minute
   		168

   
   

   =	238 × 1000	×	3	kmph
   	168		50

   
   = 85 kmph

---