426. A car travels 80 km. in 2 hours and a train travels 180 km. in 3 hours. The ratio of the speed of the car to that of the train is :

1. 1. 2 : 3

   
   
   

   2. 3 : 2

   
   
   

   3. 3 : 4

   
   
   

   4. 4 : 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed =	Distance
   	Time

   
   ∴  Speed of car : Speed of train
   

   =	80	:	180	= 40 : 60 = 2 : 3
   	2		3

   Correct Option: A

   Speed =	Distance
   	Time

   
   ∴  Speed of car : Speed of train
   

   =	80	:	180	= 40 : 60 = 2 : 3
   	2		3

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427. Two trains of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/h. The faster train passes, the slower train in 36 seconds. The length of each train is :

1. 1. 82 m

   
   
   

   2. 50 m

   
   
   

   3. 80 m

   
   
   

   4. 72 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the length of each train be x metre.
   Relative speed = 46 – 36 = 10 kmph
   

   =	10 × 5	metre/second
   	18

   
   

   =	25	metre/second
   	9

   
   

   ∴	2x	= 36
   	(25/9)

   
   

   ⇒  2x =	36 × 25	= 100
   	9

   
   ⇒  x = 50 metre

   Correct Option: B

   Let the length of each train be x metre.
   Relative speed = 46 – 36 = 10 kmph
   

   =	10 × 5	metre/second
   	18

   
   

   =	25	metre/second
   	9

   
   

   ∴	2x	= 36
   	(25/9)

   
   

   ⇒  2x =	36 × 25	= 100
   	9

   
   ⇒  x = 50 metre

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428. Two trains start from a certain place on two parallel tracks in the same direction. The speed of the trains are 45 km/hr and 40 km/hr respectively. The distance between the two trains after 45 minutes will be

1. 1. 2 km 500 m

   
   
   

   2. 2 km 750 m

   
   
   

   3. 3 km 750 m

   
   
   

   4. 3 km 250 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   Relative speed = 45– 40 = 5 kmph
   

   ∴  Required distance =		5 ×	45		km
   			60

   
   

   =	15	km = 3 km 750
   	4

   Correct Option: C

   Relative speed = 45– 40 = 5 kmph
   

   ∴  Required distance =		5 ×	45		km
   			60

   
   

   =	15	km = 3 km 750
   	4

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429. A boy started from his house by bicycle at 10 a.m. at a speed of 12 km per hour. His elder brother started after 1 hr 15 mins by scooter along the same path and caught him at 1.30 p.m. The speed of the scooter will be (in km/hr)

1. 1. 4.5

   
   
   

   2. 36

   
   
   

   3. 18	2
      	3

   
   
   

   4. 9

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the speed of Scooter be x Distance covered by cycling in
   

   3	1	hours = Distance covered by scooter in
   	2

   
   

   2	1	hours
   	4

   
   

   ⇒  12 ×	7	= x ×	9
   	2		4

   
   

   ⇒  x =	12 × 7 × 2
   	9

   
   

   =	56	= 18	2	kmph
   	3		3

   Correct Option: C

   Let the speed of Scooter be x Distance covered by cycling in
   

   3	1	hours = Distance covered by scooter in
   	2

   
   

   2	1	hours
   	4

   
   

   ⇒  12 ×	7	= x ×	9
   	2		4

   
   

   ⇒  x =	12 × 7 × 2
   	9

   
   

   =	56	= 18	2	kmph
   	3		3

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430. A policeman goes after a thief who has 100 metres start, if the policeman runs a kilometre in 8 min, and the thief a km in 10 min, the distance covered by thief before he is over-powered is

1. 1. 350 m

   
   
   

   2. 400 m

   
   
   

   3. 320 m

   
   
   

   4. 420 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   Relative speed =	1000	−	1000
   	8		10

   
   

   =	5000 − 4000	=	1000	m/minute
   	40		40

   
   

   ∴  Required time =	100
   	1000
   	40

   
   

   =	4000	= 4 m/minute
   	1000

   
   

   ∴   Distance covered by the thief =	1000	× 4
   	10

   
   = 400 metres

   Correct Option: B

   Relative speed =	1000	−	1000
   	8		10

   
   

   =	5000 − 4000	=	1000	m/minute
   	40		40

   
   

   ∴  Required time =	100
   	1000
   	40

   
   

   =	4000	= 4 m/minute
   	1000

   
   

   ∴   Distance covered by the thief =	1000	× 4
   	10

   
   = 400 metres

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