Q 1-Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively . What time will they take to be 8.5 km apart , if they walk in the same direction ?

A - 4 hrs 15 min

B - 8 hrs 30 min

C - 16 hrs

D - 17 hrs

Answer - D

Explanation

"To be 0.5 km apart , hey take 1 hour

To be 8.5 km  apart , they  take (1/0.5×8.5)  hrs= 17 hrs.
"

Q 2-A is twice as fast as B and B is thrice as fast as C is. The journey covered by C in 54 minutes will be covered by B in :

A - 18 min

B - 27 min

C - 38 min

D - 9 min

Answer - A

Explanation

"Let C's speed = x km/hr, Then , 
B's speed = 3x km/hr and 
A's speed = 6x km/hr
∴      Ratio of speed of A, B, C  = 6x:3x:x  = 6 : 3 : 1

Ratio of time taken  = 1/6:1/3:1 =  1 : 3 : 6

If C takes 6 min., then B takes 2 min.

If C takes 54 min, then B takes (2/6×54)  min = 18 min.
"

Q 3-It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car . It takes 20 minutes more ,if 200 km is done by train and the rest by car . The ratio of the speed of the train to that of the car is :

A - 2 : 3

B - 3 : 2

C - 3 : 4

D - 4 : 3

Answer - C

Explanation

"Let the speed of the train be x km/hr and hat of the car be y km/hr.

Then , 120/x+480/y=8 or  1/ x+4/y=1/15  ................................................(I)

And    200/x+400/y=25/3  or 1/x+2/y=1/24 .............................................(II)

Solving (I) and (II) , we get x=60andy=80 .

∴      Ratio of speed  = 60 : 80 = 3 : 4.
"

Q 4-If a person walk at 14 km/hr instead of 10 km/hr , he would have walked 20 km more . The actual distance travelled by him is

A - 50 km

B - 56 km

C - 70 km

D - 80 km

Answer - A

Explanation

"Let the actual distance travelled be x km. then ,
 
x/10=x+20/14

⇔  14x= 10x+200      ⇔4x=200      ⇔    x= 50 km.
"

Q 5-Two men start together to walk to a certain destination , one a 3 kmph and another a 3.75 kmph, he latter arrives half an hour before The former. he distance is :

A - 6 km

B - 7.5 km

C - 8 km

D - 9.5 km

Answer - B

Explanation

"Let the distance be x km. Then ,

x/3−x/3.75=1/2 

⇔    2.5x−2= 3.75

⇔x=3.75/0.50=15/2 =  7.5  km
"

Q 6-With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 71/2 hours. What is the distance covered ?

A - 420 km

B - 480 km

C - 640 km

D - cannot be determined

Answer - B

Explanation

"Let the distance be x km. Then ,

x/71/2−x/8=4   ⇔ 2x/15−x/8=4   ⇔ x= 480 km.
"

Q 7-Three persons are walking from a place A to another place B. Their speeds are in the ratio of 4 : 3 : 5 . The time ratio to reach B by these persons will be :

A - 4 : 3 : 5

B - 5 : 3 : 4

C - 15 : 9 20

D - 15 : 20 : 12

Answer - D

Explanation

"Ratio of speeds = 4 : 3 : 5

∴    Ratio of times taken = 1/4:1/3:1/5 =  15 : 20 : 12
"

Q 8-In covering a distance of 30 km. Abhay takes 2 hours more than Sameer . If Abhay doubles his speed ,then he would take 1 hour less than Saneer , Abhay's speed is :

A - 5 kmph

B - 6 kmph

C - 6.25 kmph

D - 7.5 kmph

Answer - A

Explanation

"Let Abhay's speed be x km/hr.

Then, 30/x−30/2x=3   ⇔  6x= 30   ⇔ x= 5 km/hr
"

Q 9-In covering a certain distance ,the speeds of A and B are in the ratio of 3 : 4 . A takes 30 minutes more than B to reach the destination . The time taken by A to reach the destination is :

A - 1 hour

B - 11 /2hours

C - 2 hours

D - 2 1/2hours.

Answer - C

Explanation

"Ratio of speeds = 3 : 4 Ratio of times taken = 4 : 3

Suppose A takes 4xx hrs and B takes 3x hrs to reach the destination. Then ,

4x−3x=30/60=1/2orx= ½

∴     ime taken by  A = 4x hrs.=  (4×1/2)  hrs =  2 hrs.
"

Q 10-Excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 45 mph. For how many minutes does the bus stop per hour ?

A - 9

B - 10

C - 12

D - 20

Answer - B

Explanation

"Due to stoppages , it covers 9 km less.

Time taken to cover 9 km = (9/54×60)  min = 10 min.
"

Q 11-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 - C

Explanation

"Let speed of the car be x kmph.

Then , speed of the train = 150/100x=(33/2x)  kmph

∴    75/x−75/3/2x= 125/10×60

⇔  75/x −50/x= 5/24      ⇔x=(25×24/5)  = 120 kmph.
"

Q 12-A car travels from P to Q at a constant speed . If its speed were increased by 10 km/hr it would have taken one hour lesser o cover the distance . It would have taken further 45 minutes lesser if the speed was further increased by 10 km/hr. What is the distance between the two cities. ?

A - 420 km

B - 540 km

C - 600 km

D - 650 km.

Answer - A

Explanation

"Let distance  =  x km and usual rate = y kmph. Then 

x/y−x/y+10=1or y(y+10)=  10x  .........................................(I)

And , x/y−x/y+20=7/4   ory(y+20)= 80x/7 ..............................(II)

On dividing (I) by (II) , we get  y = 60.

Substituting  y = 60   in (I) , we get x =  420 km.
"

Q 13-A man covered a certain distance at some speed . Had he moved 3 kmph faster , he would have taken 40 minutes less . If he had moved 2 kmph slower , he would have taken 40 minutes more . The distance (in km) is

A - 35

B - 36 2/3

C - 37 1/2

D - 40

Answer - D

Explanation

"Let distance = x km and usual rate = y kmph.

x/y−x/y+3=40/60   or 2y(y+3)=9x .............................................(I)

and ,x/y−2−x/y=40/60  or y/(y−2)= 3x   .........................................(II)

On dividing (I) by  (II), we get x = 40 km.
"

Q 14-If a train runs at 40 kmph, it reaches its destination late by 11 minutes but if it runs at 50 kmph , it is late by 5 minutes only . The correct time for the rain to complete its journey is :

A - 13 min.

B - 15 min.

C - 19 min.

D - 21 min.

Answer - C

Explanation

"Let the correct time to complete the journey  be x min.

Distance covered in (x+11)  min. at 40 kmph 
= Distance covered in (x+5) min. at 50 kmph.

∴    (x+11)/60×40=(x+5)/60×50      ⇔   x = 19 min.
"

Q 15-Robert is travelling on his cycle and has calculated to reach point A at 2 p.m. . if he ravels at 10 kmph ; he will reach here at 12 noon if he travels at 15 mph at what speed must he travel to reach A at 1 p.m.

A - 8 kmph

B - 11 kmph

C - 12 kmph

D - 14 kmph

Answer - C

Explanation

"Let the distance travelled be x km

Then , x/10−x/15=2   ⇔  3x−2x=60     ⇔    x=60

Time taken to travel 60 km at 10 km/hr = (60/10)hrs=6hrs

So, Rebert started 6 hours before 2 P.M.  i.e.  at  8 A.M.

∴     Required speed =  (60/5) kmph = 12 kmph.
"

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