176. A moving train passes a platform 50 metres long in 14 seconds and a lamp-post in 10 seconds. The speed of the train is

1. 1. 24 km/hr.

   
   
   

   2. 36 km/hr.

   
   
   

   3. 40 km/hr.

   
   
   

   4. 45 km/hr.

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Suppose length of train be x
   According to question
   

   x + 50	=	x
   14		10

   
   ⇒  14x = 10x + 500
   ⇒  4x = 500
   

   ⇒  x =	500	= 125 m
   	4

   
   Therefore, speed
   

   =	125	×	18	= 45 kmph
   	10		5

   Correct Option: D

   Suppose length of train be x
   According to question
   

   x + 50	=	x
   14		10

   
   ⇒  14x = 10x + 500
   ⇒  4x = 500
   

   ⇒  x =	500	= 125 m
   	4

   
   Therefore, speed
   

   =	125	×	18	= 45 kmph
   	10		5

---

177. If a train runs at 40 km/hour, it reaches its destination late by 11 minutes. But if it runs at 50 km/hour, it is late by 5 minutes only. The correct time (in minutes) for the train to complete the journey is

1. 1. 13

   
   
   

   2. 15

   
   
   

   3. 19

   
   
   

   4. 21

   
   
   

---

1. View Hint View Answer Discuss in Forum

   If the distance be x km, then

   x	−	x	=	6
   40		50		60

   
   

   ⇒	x	−	x	= 1
   	4		5

   
   ⇒  x = 20 km.
   

   ∴   Required time =		20		hour – 11 minutes
   		40

   
   

   =		1	× 60 − 11		minutes
   		2

   
   = 19 minutes

   Correct Option: C

   If the distance be x km, then

   x	−	x	=	6
   40		50		60

   
   

   ⇒	x	−	x	= 1
   	4		5

   
   ⇒  x = 20 km.
   

   ∴   Required time =		20		hour – 11 minutes
   		40

   
   

   =		1	× 60 − 11		minutes
   		2

   
   = 19 minutes

---

---

178. A student rides on bicycle at 8 km/hour and reaches his school 2.5 minutes late. The next day he increases his speed to 10 km/ hour and reaches school 5 minutes early. How far is the school from his house ?

1. 1. 5	km
      8

   
   
   

   2. 8 km

   
   
   

   3. 5 km

   
   
   

   4. 10 km

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let x km. be the required distance.
   Difference in time = 2.5 + 5 = 7.5 minutes
   

   =	7.5	hrs. =	1	hrs.
   	60		8

   
   

   Now,	x	−	x	=	1
   	8		10		8

   
   

   ⇒	5x − 4x	=	1
   	40		8

   
   

   ⇒  x =	40	= 5 km.
   	8

   
   
   Second Methdod :
   Here, S₁ = 8, t₁ = 2.5
   S₂ = 10, t₂ = 5
   

   Distance =	(S1 ×S2)(t1 + t2)
   	S2 −S1

   
   

   =	(8 × 10)(2.5 + 5)
   	10 − 8

   
   

   = 40 ×	7.5	= 5 km
   	60

   Correct Option: C

   Let x km. be the required distance.
   Difference in time = 2.5 + 5 = 7.5 minutes
   

   =	7.5	hrs. =	1	hrs.
   	60		8

   
   

   Now,	x	−	x	=	1
   	8		10		8

   
   

   ⇒	5x − 4x	=	1
   	40		8

   
   

   ⇒  x =	40	= 5 km.
   	8

   
   
   Second Methdod :
   Here, S₁ = 8, t₁ = 2.5
   S₂ = 10, t₂ = 5
   

   Distance =	(S1 ×S2)(t1 + t2)
   	S2 −S1

   
   

   =	(8 × 10)(2.5 + 5)
   	10 − 8

   
   

   = 40 ×	7.5	= 5 km
   	60

---

179. If a man reduces his speed to 2/3, he takes 1 hour more in walking a certain distance. The time (in hours) to cover the distance with his normal speed is :

1. 1. 2

   
   
   

   2. 1

   
   
   

   3. 3

   
   
   

   4. 1.5

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Since man walks at 2/3 of usual speed, time taken will be 3/2 of usual time.
   

   ∴	3	of usual time = usual time + 1 hour.
   	2

   
   

   ⇒		3	− 1		of usual time = 1
   		2

   
   ⇒   usual time = 2 hours.

   Correct Option: A

   Since man walks at 2/3 of usual speed, time taken will be 3/2 of usual time.
   

   ∴	3	of usual time = usual time + 1 hour.
   	2

   
   

   ⇒		3	− 1		of usual time = 1
   		2

   
   ⇒   usual time = 2 hours.

---

---

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

1. 1. 72 m

   
   
   

   2. 80 m

   
   
   

   3. 82 m

   
   
   

   4. 50 m

   
   
   

---

1. View Hint View Answer Discuss in Forum

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

   =		10 × 5		m./sec.
   		18

   
   

   =	25	m./sec.
   	9

   
   

   ∴	2x					= 36
   	25
   	9

   
   

   ∴  2x = 36 ×	25	= 100
   	9

   
   

   ⇒  x =	100	= 50 metre
   	2

   Correct Option: D

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

   =		10 × 5		m./sec.
   		18

   
   

   =	25	m./sec.
   	9

   
   

   ∴	2x					= 36
   	25
   	9

   
   

   ∴  2x = 36 ×	25	= 100
   	9

   
   

   ⇒  x =	100	= 50 metre
   	2

---