*Time and Distance - Solved Problems 2*
21. A monkey could climb
3 meters of the around wet pole in the first minute but slipped down 1 meter in the
next minute. The climbing and slipping occur every alternate minute. What time
will the monkey take to reach the top of the pole which is 31 meters long?

a)25 minutes b)29 minutes c)30
minutes d)32 minutes

**Answer : B**

**Explanation :**Every 2 minutes, the monkey climbs (3-1) = 2 meters.

In 28 minutes, it will
climb 28 meters.

Remaining height to climb is = (31-28)
= 3 meters

In the 29

^{th}minute, the monkey will cover the last 3 minutes and reach the top of the pole.
22.A man takes 8 hours
walking to a certain place and riding back. He would have gained 2 hours by riding
both ways. What time would he take to walk both ways?

a)4 hours b)8 hours c)10
hours d)12 hours

**Answer : C**

**Explanation :**Time taken in walking one way and riding back (W+R)= 8 hours.

Time taken in riding both
ways 2R= 2 hours less than W+R = 8-2 = 6 hours.

Time taken to
ride one-way R=

6
2

= 3 hours
Time taken in walking 1 way = (Walk
in 1 way + Ride in 1 way) – Ride in 1 way

= (8 -3) = 5 hours

Time taken in walking two ways = (5 +
5) = 10 hours.

23.Two cars P and Q
start from the same point and move in the opposite direction at speeds of 35
kmph and 30 kmph. After how much time they will meet if the distance between
the P and Q is 357.5 kilometers?

a)4 hours b)
5 hours c)5 hours 30 minutes d)6
hours

**Answer:C**

**Explanation:**Two cars are moving in the opposite direction; their relative speed is the sum of their speeds.

Relative Speed = 35 kmph + 30
kmph = 65 kmph

Distance between P and Q =
357.5 kilometers

Time =

Distance
Speed

=
357.5
65

= 5.5 hours
They will meet after 5.5 hours

24. A and B are
travelling in the same direction, and A is 200 meters ahead of B. Speed of A is
12 m/s, and the speed of B is 8m/s. How
much would be the distance between them after 15 more seconds?

a)
160m b)140 m c)260 m d)300m

**Answer :C**

**Explanation:**Initially, the distance between A and B is 200 meters.

A and B both are
moving in the same direction, and their relative speed is the difference in
their speeds.

Relative speed = (12-8)= 4 m/s.

Means in every
second, A travels 4 meters more than B.

In
15 seconds, A will increase his lead by ( 15 x 4) = 60 meters.

Therefore, after
15 more seconds, the distance between A and B will be

(200meters + 60
meters )=260 meters

25.The distance between
Bangalore and Kakinada is 1000 km. A car starts from Bangalore towards Kakinada
at 6 a.m at an average speed of 60 km/h. Another car starts from Kakinada
towards Bangalore at the same time at an average speed of 40 kmph. How far from Bangalore will the two cars meet?

a)
400 km b)600 km c)550
km d)450 km

**Answer: B**

**Explanation:**The distance between two cities = 1000 km

Speed of the Car starts from Bangalore=
60 kmph

Speed of the car starts from Kakinada
= 40 kmph

Two cars are travelling in the opposite
direction, relative speed =(60+40) = 100 kmph.

Time taken to meet each other =

Distance
Speed

=
1000
100

= 10 hours
Car
started from Bangalore travelled 10 hours.

Therefore, distance from Bangalore= Speed of
the car started from Bangalore x Time

= (60 x 10) = 600 km

26.Two vehicles A and B
are travelling towards each other from two different places 198 kms apart. The
ratio of the speed of the vehicles A and B is 5:6, and the speed of the vehicle
A is 60 kmph. After what time will the two vehicles meet each other?

a)
30 min b) 45 min c)1
hour d)1 hour 30 minutes

**Answer: D**

**Explanation :**Given that speed of the vehicle A= 60 kmph

The ratio of the speeds of A and B
= 5:6

Speed of vehicle A =
5x=60

Now speed of vehicle B = 6x= 72
kmph => x = 12 kmph

As both vehicles are travelling towards each other,
they are moving in the opposite direction => Relative speed = (60+72)= 132 kmph

Time taken to meet each other =

Distance between two places
Relative Speed

=

198
132

=1.5 hours.
Therefore, two
vehicles meet other after 1 hour 30 minutes

27.A thief steals a
motorbike at 8 a.m and rides the bike at an average speed of 40 kmph. The theft
was discovered at 9.30 a.m, and the policeman started chasing on another bike
at a speed of 70kmph. When will he catch the thief?

a)
10.30 a.m b)11.30 a.m c)12 noon d) He cannot catch him at all

**Answer: B**

**Explanation :**Thief stole the car at 8 a.m and rides at a speed of 40 kmph

The theft was
discovered at 9.30 a.m

In
1 hour 30 minutes, thief travels = (40 x 1 hour 30 minutes) = 60 km.

Therefore,
the thief was 60 km ahead of the policeman.

At
9.30, the policeman started chasing at a speed of 70 kmph.

As
they both are moving in the same direction, their relative speed = (70-40) = 30
kmph

Time taken by the policeman to cover 60 km
travelled by thief already =

Distance
Relative Speed

=

60
30

= 2 hours.
Two
hours after 9.30 a.m, the thief will be caught at 11.30 am.

28.A businessman travels
600 km in 8 hours, partly by train and partly by his car, If he had travelled
by all the way by train, he would have saved

2
3

of the time he travelled in
his car and would have reached 3 hours earlier. What is the distance covered by
the car ?
a)
250 km b)220 km c)180
km d)100 km

**Answer:C**

**Explanation :**Difference in a time of 1 ho9ur is due to saving in time, resulting from that distance being covered by the train instead of the car.

2
3

rd time in car = 3
hour
Total time in car= 3 x

3
2

= 4.5 hours
Time spend in train journey = ( 8 - 4.5)=
3.5 hours.

If tota distance
were covered by train, the time taken is ( 8 – 3) = 5 hours.

In 5 hours, the distance covered by
train is 600 km.

In 3.5 hours , distance covered
by train =

600
5

x 3.5=420 km.
Therefore, the distance covered by car= (600-
420) = 180 km

29. A man wants to cover
a distance of 45 km on his bicycle, and his speed is 15 kmph. After 9 km, he
takes rest for 15 min. How long will he take to cover the whole distance?

a)
4 hours b)4
hours 15 minutes c)5 hours d)5 hours 15
minutes

**Answer:A**

**Explanation :**Speed of the cyclist = 15 kmph

Total distance to
be covered =45km

Therefore time taken by him to cover 45
km=

Distance
Speed

=
45
15

= 3 hours.
The cyclist has taken rest after
every 9 km, so in total, he took rest 4 times.

The
rest time = 4 x 15 minutes = 1 hour

So, total time = (3 hours + 1 hour) = 4 hours

30.Vehicle A starts from
P to Q, and another vehicle B starts from Q to P. Both vehicles meet each other
at the midpoint of P and Q. After they meet each other, they complete their
remaining journey in 3 hours and 2 hours,
respectively. What is the ratio of the time taken by both vehicles for the whole
journey ?

a)
2 :3 b)3:2 c)8:5 d)9:4

**Answer : B**

**Explanation :**Time taken by vehicle B to cover half the distance = 3 hours

Therefore, time taken by
vehicle A to cover complete distance= (2 x 3)= 6 hours

Time taken by vehicle B to cover half the
distance = 2 hours

Time taken by Vehicle B to cover total
distance = (2 x 2) = 4 hours.

Therefore, the ratio of times taken
by vehicle A to vehicle B for the whole journey

= 6 hours: 4 hours
= 3:2

31. Two
guns were fired from the same place at an interval of 15 minutes. A person in a
car approaching the place hears the 2

^{nd}13 minutes after the 1^{st}. Find the speed of the car, if the sound travels at 80 m/s.
a)
15 m/s b)14 m/s c)12.3 m/s d)11.5
m/s

**Answer: C**

**Explanation:**If the car were not moving, the person would have heard the two sounds at an interval of 15 minutes.

The distance travelled by car in 13
minutes is equal to the distance travelled by sound in (15-13 )= 2 minutes.

Distance travelled by sound in 2
minutes = (80 x 120 sec) =9600 meters

So the distance travelled by car in 13
minutes is 9600 meters.

Therefore in 1 second , the car travels =

9600
(13x60)

) =12.3 meters
Therefore, the speed of the car =
12.3 mps

32. Sudheer
driving in the morning fog passes a pedestrian who was walking at the rate of 2
km/h in the same direction. The pedestrian can see the car for 6 minutes and up
to a distance of 0.8 km. Find the speed of the car?

a)
8kmph b)10 kmph c)12 kmph d)12.5 kmph

**Answer : B**

**Explanation :**Time is 6 minutes =

6
60

hours =
6
60

hours
Distance covered
by man in 6 minutes = 2 kmph x 1/10 =
0.2 km

Distance covered by the car
in 6 minutes = (0.2 km + 0.8 km) = 1 km

Speed of the car =

Distance
Time

= 1
km/6 minutes =10 kmph**Alternate Method :**

Let the speed of the
car be x. and Speed of car= 2 kmph

Time is 6
minutes =

6
60

hours =
1
10

hours
Sudheer and pedestrian are moving
in same direction=> Relative speed= x-2

Speed
= Distance by time

x-2 =

0.8

=> x= 10 kmph
1
10

33.A car starts from A
towards B, and another starts from B towards A. The distance between A and B is
180 km. If the two cars travel in the same direction ( from A towards B), they
will meet after 6 hours, and if they travel in the opposite direction, they
will meet after 2 hours. What is the speed of the car starting from A?

a)
55 kmph b)58 kmph c)60
kmph d)72 kmph

**Answer :C**

**Explanation:**According to the question,

Let the speed of the car starts from A
is x, and the speed of the car starts from B is y.

the distance between two places is 180 km

Time taken to cover 180 km distance when
they move in the opposite direction = 2 hours

So their relative speed = ( x +
y) =

180
2

= 90 kmph
Time taken to
cover 180km distance when they move in the same direction is 6 hours.

Then relative speed = ( x – y)=

180
6

= 30 kmph
On solving ( x + y)=90 and ( x – y)= 30 , we get x=60
kmph.

34.Sharma started going
for a morning walk every day. The distance he walked on the first day is 4 kms.
Every day Sharma walks half of the distance he walked on the previous day. What
can be the maximum total distance he walked in his lifetime?

a)
20 km b)12 km c)10 km d) 8 km

**Answer : D**

**Explanation:**The distance walked by Sharma on the first day= 4 kms.

Every day he walks half the distance he walked
the previous day.

Therefore, the distance walked =
4+2+

1
2

+
1
4

+ ….
The series is in G.P. First-term a=4 and common ratio=

1
2

.
The maximum total distance walked by Sharma in
his lifetime would be infinite. Hence, the series would be an infinite
Geometric series.

Sum of the terms of infinite
geometric series =

a
1-r

=
4
(1-

= 8 kms
1
2

)
35. Ravi starts walking
from A towards B , covers a distance of 67 km at the rate of 13 kmph. An hour
later, Ram starts his journey at B towards A and walks at the rate of 5
kmph . Where will Ravi meet Ram from B?

a)
12 km b)15 km c)18
km d)21 km

**Answer:B**

**Explanation:**Ravi covered 13 km distance in 1 hour.

Remaining distance = (67 km – 13 km)=
54 km

Now speeds
of Ravi and Ram are 13 kmph and 5 kmph, and they travel in the opposite
direction

Therefore they together cover
(13 +5) = 18 km in one hour.

Time taken to cover remaining
54 km =

Distance
Speed

=
54
18

= 3 hours.
Therefore, they meet at a distance
of (3 x 5) = 15 km from B.