Time and Distance problems
- 1. A train Meerut at 6 a.m. and reaches Delhi at 10 a.m. another train leaves Delhi at 8 a.m. and reaches Meerut at 11:30 a.m. at what time do trains cross one another?
Options- A. 9.26 a.m.
- B. 9 a.m.
- C. 8:36 a.m.
- D. 8:56 a.m. Discuss
Correct Answer: 8:56 a.m.
Explanation:
Let the distance between Meerut and Delhi be y km.
Average speed of the train leaving Meerut = y/4 km/hr.
Average speed of the train leaving Delhi = 2y/7 km/hr.
suppose they meet x hrs. after 6 a.m
then, xy/4 + 2y (x-2)/7 = y
? x/4 + 2x-4/7 = 1
? 15x = 44
? x = 44/15 = 2 hrs. 56 min
So, the train meet at 8:56 a.m
- 2. A train leaves Delhi at 5 a.m. and reaches Kanpur at 10 a.m. another train leaves Kanpur at 7 a.m. and reaches Delhi at 2 p.m. at what time do the two trains meet?
Options- A. 8:45 a.m.
- B. 3:45 p.m.
- C. 6:45 a.m.
- D. data inadequate Discuss
Correct Answer: 8:45 a.m.
Explanation:
Let the distance between Delhi and Kanpur be y km .
Suppose the train leaving from Delhi is A and the train leaving from Kanpur B
A's speed = y/ (10 a.m - 5 a.m) = y/5 km/hr.
B's Speed = y/ (2 p.m - 7 a.m) = y/7 km/hr.
Since B starts two hours later than A, the distance already covered by A at the start of B = 2y/5 km.
Remaining distance = y- 2y/5 = 3y/5 km.
Relative speed of approach of two trains = (y/5 + y/7)
= 12y/35 km/hr.
Time taken to cover the remaining distance by both trains = (3y / 5) / (12y / 35)
= (3/5) x (35/12) = 7/4 hrs.
= 1 hr. 45 min.
? The two train will meet at (7 a.m + 1hr.45 min)
= 8.45 a.m
- 3. A start from P walk to Q a distance of 51.75 kilometer at the rate of 3.75 km an hour. An hour latter B starts from Q for P and walk at the rate of 4.25 km an hour. When and where will A meet B?
Options- A. 26.25 km. from Q
- B. 25.50 km. from Q
- C. 25.30km. from P
- D. can't be determined Discuss
Correct Answer: 25.30km. from P
Explanation:
A has already gone 3.75 km when B starts of the remaining 48 km.
A walks 3.75 km and B walks 4.25 km in one hour in opposite direction i.e., they together pass over (3.75 + 4.25) = 8 km. in hour.
Therefore , 48 km. are passed over in 48/8= 6 hours.
? A meets B in 6 hours after B started and, therefore, they meet at a distance of (4.25 X 6 ) = 25.5km. from Q.
- 4. Two boys begin together to write out a booklet containing 817 lines. The first boy start with first line, writing at rate of 200 lines an hour and the second boys start with a last line. He writes line 817 and so on backwards proceeding at the rate of 150 lines an hour. An what line will they meet?
Options- A. 466th
- B. 465th
- C. 467th
- D. 468th Discuss
Correct Answer: 467th
Explanation:
Let the two meet at the Nth line
From the question
Nth/200 = (817 - Nth)/150
? 3Nth = 4(817-Nth)
? Nth = (4 x 817) / 7
? Nth = 466.85
So, they will meet at the 467th line
- 5. Two car A and B are running toward each other from two different place 88 km apart. If the ratio of the speed of the car A and B is 5:6 and the speed of the car B is 90 km per hour, after how long will the two meet each other?
Options- A. 26 min.
- B. 24 min.
- C. 32 min.
- D. 36 min. Discuss
Correct Answer: 32 min.
Explanation:
Speed of the car A = (5 / 6) x 90
= 75 km/hr.
? Required time = [ 88 / (90 +75)] x 60
= 32 minutes
- 6. In a circus there was a leopard and a tiger walking in the two different rings of same radii. There I observed that when leopard moved 3 steps, tiger moved 5 steps in the same time,but the distance traversed by leopard in 5 step is equal to the distance traversed by tiger in 4 steps. what is the number of rounds that a leopard made when tiger completed 100 rounds?
Options- A. 120
- B. 48
- C. 75
- D. none of these Discuss
Correct Answer: 48
Explanation:
The ratio of speeds = The ratio of distances, when time is constant
? The ratio of distance covered by leopard to the tiger = 12 : 25
Again, ratio of rounds made by leopard to the tiger = 12 : 25
hence, leopard makes 48 rounds, when tiger makes 100 rounds
- 7. A thief sees a jeep at a distance of 250 m, coming towards him at 36 km/h. Thief takes 5 seconds to realise that there is nothing but the police is approaching him by the jeep and start running away from police at 54 km/h. But police realise after 10 seconds, when the thief starts running away, that he is actually a thief and gives chase at 72 km/h. how long after thief saw police did police catchup with him and what is the distance police had to travel to do so?
Options- A. 50 sec, 1000 m
- B. 65 sec, 1150 m
- C. 65 sec, 1300 m
- D. 45 sec, 1050 m Discuss
Correct Answer: 65 sec, 1150 m
Explanation:
Initial speed of police = 10 m/s
Increased speed of police = 20 m/s
Speed of thief = 15 m/s
Initial difference between thief and police = 250 m
After 5 seconds difference between thief and police = 250 - (5 x 10) = 200 m
After 10 seconds more, the difference between thief and police = 200 + (5 x 10) = 250 m.
Now, the time required by police to catch the thief = 250/5 = 50 s
Distance travelled = 50 x 20 = 1000 m
Total time = 50 + 15 = 65 sec
Total distance = 1000 + (15 x 10) = 1150 m
- 8. Den Bosh and Eastbourne are two famous cities 300 km apart. Maradona starts from Den Bosch at 8 : 24 am. An hour later Pele starts from Den Bosch. After travelling for 1 hour, Pele reaches Nottingham that Maradona had passed 40 minutes earlier. Nottingham falls on the way from Den Bosh to Eastbourne at the same time, what is the speeds of the time Maradona and Pele respectively?
Options- A. 100 km/h, 125 km/h
- B. 60 km/h, 80 km/h
- C. 60 km/h, 75 km/h
- D. 75 km/h, 100 km/h Discuss
Correct Answer: 75 km/h, 100 km/h
Explanation:
Let pele covers D km in 1 hours. So Maradona takes (2 h - 40 min) = 1 h 20 min to cover D km.
Let speed of Maradona and pele be M and P respectively than.
D = M x 4/3 and D = P x 1
M/P = 3/4
Again, 300/M - 300/P = 1
300/3k - 300/4k = 1
k = 25
M = 3k = 75 km/h and
P = 4k = 100 km/h
- 9. Soniya and Priyanka started from Amethi and Bellari for Bellari and Amethi, which are 645 km apart. They meet after 15 hours. After their meeting, Sonia increased her speed by 3 km/h and priyanka reduced her speed by 3 km/h, they arrived at Bellari and Amethi respectively at the same time. What is their initial speeds?
Options- A. 24 km/h and 30 km/h
- B. 25 km/h and 18 km/h
- C. 18 km/h and 21 km/h
- D. 20 km/h and 23 km/h Discuss
Correct Answer: 20 km/h and 23 km/h
Explanation:
The sum of their speeds = 615/15 = 43 km/h
Notice that they are actually exchanging their speeds. Only then they can arrive at the same time at their respective destinations.It means the difference in speeds is 3 km/h.
Thus, x + ( x + 3) = 43
x = 20 and x + 3 = 23
The concept is very similar to the case when after meeting each other they returned to their own places of departure. It can be solved through option also.
- 10. A tiger is 50 of its own leaps behind a deer. The tiger takes 5 leaps per minute to the deer's 4. If the tiger and the deer cover 8 m and 5 m per leap respectively, what distance will the tiger have to run before it catches the deer?
Options- A. 600 m
- B. 700 m
- C. 800 m
- D. 1000 m Discuss
Correct Answer: 800 m
Explanation:
Speed of tiger = 40 m/min
Speed of dear = 20 m/min
Relative speed = 40 - 20 = 20 m/min
Difference in distance = 50 x 8 = 400 m
? Time taken in overtaking (or catching) = 400/20 = 20min
? Distance travelled in 20 min = 20 x 40 = 800 m
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