TIME SPEED AND DISTANCE

            Q1. Sujal and Varun are 50 km apart and started to walk towards each other, Sujal walked at the rate of 10 km/hr and Varun at 5 km/hr. In what time will they meet?

                  (a)  3 hrs and 20 min       (b)  6 hrs           

                  (c)  3 hrs and 40 min       (d)  3 hrs           

            Q2. Ravi runs after Bhuvan who is 1500 m ahead of him. If speed of Ravi is 30 km/hr and that of Bhuvan is 10 km/hr, in how much time will Ravi catch Bhuvan?

                  (a)  0.05 hrs                     (b)  0.075 hrs    

                  (c)  0.025 hrs                   (d)  0.055 hrs    

            Q3. A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?

                  (a)  200                            (b)  240 

                  (c)  300                            (d)  420 

            Q4. Two trains, 200 and 100 meters long take 30 seconds to cross each other while traveling in the same direction and take only 10 seconds when they cross in opposite directions. What are the speeds at which the trains are traveling?

                  (a)  20 m/s and 5 m/s      (b)  20 m/s and 10 m/s

                  (c)  10 m/s and 5 m/s      (d)  40 m/s and 20 m/s

            Q5. A train traveling at 100 kmph overtakes a Car traveling at 50 km/hr in 40 seconds. What is the length of the train in meters?

                  (a)  555.55                       (b)  550.5          

                  (c)  525                            (d)  445.5          

            Q6. Ram and Mohan start at the same time from A to B to go to B and A, a distance of 63 km at the rates of 3 km/hr and 4 km/hr. They meet at X, then go to B and A and return immediately and meet again at Y. find the distance XY

                  (a)  21  (b)                        15 

                  (c)  24  (d)                        18 

            Q7. Samir traveled the first 2 hours of his journey at 40 kmph and the remaining 3 hours of his journey at 80 kmph. What is his average speed for the entire journey?

                  (a)  62  (b)                        60 

                  (c)  50  (d)                        64 

            Q8. Sajal can swim with the stream at the rate of 15 km/hr and 10 km/hr against the stream; find his speed in still water.

                  (a)  12.5                           (b)  12   

                  (c)  11.5                           (d)  15   

            Q9. A boat travels from point A to point B upstream and returns from point B to point A downstream. If the round trip takes the boat 10 hours and the distance between point A and point B is 100 km and the speed of the stream is 5 km/hr, what is the speed of the boat?

                  (a)  22.5                           (b)  24.3

                  (c)  25.5                           (d)  23.5

            Q10. In a kilometer race, A can give B a start of 200 m or 2 minutes seconds. How long does A take to complete the race?

                  (a)  320 sec                     (b)  480 sec      

                  (c)  360 sec                     (d)  600 sec      

            Q11. Steve and Martin walk around a circular path of circumference 1200 meters. Steve walks at speed of 80 m/min and Martin at a speed of 60 m/min. if they start at the same point and walk in the same direction, When will they meet at the starting point?

                  (a)  60 min                       (b)  65 min        

                  (c)  40 min                       (d)  20 min        

            Q12. Three cyclists Harry, Randy and Mary ride around a circular course 95 km around at the rate of 8, 12 and 20 km an hour. Harry and Randy ride in the same direction and Mary in the opposite direction. In how many hours will they meet again?

                  (a)  23 hrs                        (b)  23.75 hrs    

                  (c)  23.5 hrs                     (d)  24 hrs         

            Q13. At what time between 6 and 7 will the hands of a watch coincide? 

                  (a)  32.7 min past 6         (b)  32.5 min past 6

                  (c)  32.9 min past 6         (d)  33 min past 6         

            Q14. A clock was set at noon on Sunday it gains 2 minutes in 24 hours. What will be the true time when the first clock indicates 2 pm on Tuesday?

                  (a)  1:55:00 PM                (b)  1:55:48 PM 

                  (c)  1:55:40 PM                (d)  1:55:50 PM 

                  Ans1. (a)    Relative speed = 5 + 10 = 15 km/hr

                              Time to walk 50 km = 50/15 = 3.33 hours, which is 3 hours and 20 min (approx).

                  Ans2. (b)    Relative speed = 30 – 10 =  20 km/hr 

                              Distance to be covered = 1500 m = 1.5 km

                              Time taken = 1.5/20 = 0.075 hrs.

                  Ans3. (b)    The extra time taken to cross the platform is to cross the length of the platform, therefore

Length = 72 × 12/3600 = 0.24 km = 240 meter

                  Ans4. (b)    Distance covered (sum of lengths of the train)

                              = 200 + 100 = 300 meters.

                  Let Train 1 be traveling at X m/sec and Train 2 be traveling at Y m/sec. (considering X > Y)

                              Now while traveling in same direction

                                    Time = (L₁ + L₂)/(X – Y)

                              Therefore         30 = 300/X - Y, X – Y = 10

                              Now while traveling in opposite direction

                                    Time = (L₁ + L₂)/(X + Y)

                              Therefore         10 = (L₁ + L₂)/(X + Y), X +Y = 30

                              Solving the two equations X = 20 m/sec

                                                              Y = 10 m/sec

                  Ans5. (a)    Let the car length to be zero in comparison to train, In physics it is called point object.

                              Here, Relative speed = 100 – 50 = 50 km/hr

                              Distance traveled in 40 seconds

                                    = 50 × 40/3600 = 0.55555 km

                                    = 555.55 meters

                  Ans6. (d)    First Ram and Mohan meet at X, Distance = 63 km

                              First Ram and Mohan meet at Y, Distance = 63 × 3 = 189 km

                              Speed of Ram = 3 km/hr,

                              Speed of Mohan = 4 km/hr

                              Ram travels AX distance and Mohan BX

                              Relative speed = 3 + 4 = 7 km/hr,

                              Time when they meet first = 63/7 = 9 hrs

                              In 9 hrs Ram travels 9 × 3 = 27 km = AX

                              Therefore Mohan travels = 63 – 27 – 36 = BX

                              Time when they meet second = 189/7

                                    = 27 hrs

                              In 27 hrs Ram travels 27 × 3  = 81 km

                                    = AX + XB + BY

                              Since AX + XB = 63, BY = 18 and AY = 45

                              Since AX = 27, and AY = 45. XY = 18 km

                  Ans7. (d)    Average speed = Total Distance / Total time Taken

                              Total distance = 40 × 2 + 80 × 3 = 320 km

                              Total time taken = 2 + 3 = 5 hours.

                              Average speed = 320/5 = 64 kmph

                  Ans8. (a)    Upstream speed = 15 km/hr, Downstream speed is 10 km/hr

                              Using direct formula

1/2(15 + 10) = 12.5 km/hr

                  Ans9. (b)    Total distance = 100 × 2 = 200,

                              Total time = 10 hrs

                              Average speed = 200/10 = 20 km/hr

                              Assuming speed of boat = X

                              Speed downstream

                                    = Speed of Boat + Speed of stream

                                    = X + 5

                              Speed downstream

                                    = Speed of Boat – Speed of stream

                                    = X – 5

                              Since average speed = 20, and using formula of average speed

                  20 = 2(X + 10)(X -10)/(X + 10) +(X – 10)

                              Solving for X, X = 24.35 km/hr

                  Ans10. (b)  In a 1000 meter race A gives B a start of 200 m or 2 minutes. This means that B takes 120 seconds to run 200 m. Therefore, B will take 120 × 5 = 600 seconds to run the stretch of 1000 meters. As A takes 120 seconds less than B, he will take 480 seconds to run the 1000 m.

                  Ans11. (a)  Time taken by Steve to complete one round

                                    = 1200/80 = 15 min

                              Time taken by Martin to complete one round

                                    = 1200/60 = 20 min

                              They meet again at starting point, LCM of 15 and 20 = 60 minutes

                  Ans12. (b)  Randy will meet Harry in every  95/(12 – 8) = 95/4 hrs

                              Randy and Mary will meet in every 95/(12 + 20) = 95/32 hrs

                              Harry and Mary will meet in every  95/(8 + 20) = 95/28 hrs

                              They all will meet at the LCM of the three 95/4, 95/32 and 95/28

                              LCM is 95/4 hrs.

                  Ans13. (a)  At 6, the hour hand and the minute hand are 30 minute away, the minute hand gains 1 in 12/11 minute, it will gain 30 in 12/11 × 30 = 32.7 minutes.

                              Therefore hands will coincide 32.7 min past 6.

                  Ans14. (b)  Time from noon on Sunday to 2 pm on Tuesday = 50 hours

                                    24 hrs 2 min of the first clock = 24 hrs of the correct time

                              1442 minutes = 1440 minutes

                                    1 minute = 1440/1442

                              3000 minutes (50 hrs)   =  1440/1442× 3000

                                    = 2995.8

                                    = 2995.8/60 = 49.93 hrs