One stop blog for all competitive examinations

                                  Time and Distance - Solved Problems 2 21. A monkey could climb 3 meters of the around wet pole in the ...

Quantitative Aptitude Questions - TIME AND DISTANCE Solved Questions -2

                                 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 29th 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 2nd  13 minutes after the 1st. 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 /
1 / 10
  => x= 10 kmph

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-
1 / 2
)
= 8 kms

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.