Time and Distance problems
- 1. Two persons start running simultaneously around a circular track of length 600 m from the same point at speeds of 25 kmph and 35 kmph. When will they meet for the first time any where on the track ?
Options- A. 54 sec
- B. 36 sec
- C. 72 sec
- D. 11 sec Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 36 sec
Explanation:
Time taken to meet the first time = length of track/relative speed
Given the length of the track is 600 m
The relative speed = 25 + 35 = 60 kmph = 60 x 5/18 m
Therefore Time = = 600/60 x (18/5) = 36 sec.
- 2. Radha and Hema are neighbours and study in the same school. Both of them use bicycles to go to the school. Radha?s speed is 8 km/hr whereas Hema?s speed is 10 km/hr. Hema takes 9 minutes less than Radha to reach the school. How far is the school from the locality of Radha and Hema?
Options- A. 5 km
- B. 5.5 km
- C. 6 km
- D. 6.5 km Also asked in: Bank Exams
Correct Answer: 6 km
Explanation:
- 3. Tilak rides on a cycle to a place at speed of 22 kmph and comes back at a speed of 20 kmph. If the time taken by him in the second case is 36 min. more than that of the first case, what is the total distance travelled by him (in km)?
Options- A. 132 km
- B. 264 km
- C. 134 km
- D. 236 km Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 264 km
Explanation:
Let the distance travelled by Tilak in first case or second case = d kms
Now, from the given data,
d/20 = d/22 + 36 min
=> d/20 = d/22 + 3/5 hrs
=> d = 132 km.
Hence, the total distance travelled by him = d + d = 132 + 132 = 264 kms.
- 4. In a race of 800m Kaushik gives Piyush a start of 200m and then loses the race by 20 seconds. What is the speed of Piyush and Kaushik respectively ? If the ratio of respective speeds be 3:2.
Options- A. 15 m/s
- B. 20 m/s
- C. 25 m/s
- D. 30 m/s Also asked in: Bank Clerk, Bank PO
Correct Answer: 20 m/s
Explanation:
Let the speed of Kaushik be Sk and speed of Piyush be Sp Let the time taken by Piyush be t second then, SkSp = 800t+20600t = 23 Since given ratio t = 20 s Speed of Piyush = Sp = 600/20 = 30 m/s Speed of Kaushik = 800/40 = 20 m/s
- 5. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?
Options- A. 9 : 20
- B. 11 : 9
- C. 11 : 20
- D. None of these Discuss
Correct Answer: 11 : 9
Explanation:
In the same time, they cover 110 km and 90 km respectively.
Therefore, Ratio of their speeds = 110 : 90 = 11 : 9
- 6. If a student walks at the rate of 4 mts/min from his home, he is 4 minutes late for school, if he walks at the rate of 6 mts/min he reaches half an hour earlier. How far is his school from his home ?
Options- A. 100 mts
- B. 96 mts
- C. 98 mts
- D. 120 mts Also asked in: Analyst, Bank Clerk, Bank PO, AIEEE, Bank Exams, CAT, GATE, GRE
Correct Answer: 98 mts
Explanation:
Let the distance between home and school is 'x'.
Let actual time to reach be 't'.
Thus, x/4 = t + 4 ---- (1)
and x/6 = t - 30 -----(2)
Solving equation (1) and (2)
=> x = 98 mts.
- 7. K is 50% faster than L. If L starts at 9 A.M. and K starts at 10 A.M. L travels at a speed of 50 km/hr. If L and K are 300 kms apart, The time when they meet when they travel in opposite direction is ?
Options- A. 12 pm
- B. 1 pm
- C. 11 am
- D. 11:30 am Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 12 pm
Explanation:
let 't' be the time after which they met since L starts.
Given K is 50% faster than L
50 t + 1.5*50(t-1) = 300
50 t +75 t = 300 + 75
t = 375 / 125 = 3 hrs past the time that L starts
So they meet at (9 + 3)hrs = 12:00 noon.
- 8. Jagan went to another town covering 240 km by car moving at 60 kmph. Then he covered 400km by train moving at 100 kmph and then rest 200 km he covered by a bus moving at 50 kmph. The average speed during the whole journey was ?
Options- A. 36 kmph
- B. 35 kmph
- C. 72 kmph
- D. 70 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 70 kmph
Explanation:
By car 240 km at 60 kmph
Time taken = 240/60 = 4 hr.
By train 240 km at 60 kmph
Time taken = 400/100 = 4 hr.
By bus 240 km at 60 kmph
Time taken = 200/50 = 4 hr.
So total time = 4 + 4 + 4 = 12 hr.
and total speed = 240+400+200 = 840 km
Average speed of the whole journey = 840/12 = 70 kmph.
- 9. An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 600 km from the starting point ?
Options- A. 6 hrs 24 min
- B. 6 hrs
- C. 7 hrs 21 min
- D. 6 hrs 28 min Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 6 hrs 28 min
Explanation:
Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 4 x 7 = 28 min
Hence, total time taken = 6 hrs 28 min.
- 10. Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m. ?
Options- A. 20 kmph
- B. 18 kmph
- C. 12 kmph
- D. 16 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 12 kmph
Explanation:
Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
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