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- Question
- Two ladies simultaneousely leave cities A and B connected by a strainght road and travel towards each other. The first lady travels 2km/h faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?
Options- A. 5 km,3 km
- B. 7 km, 5 km
- C. 8 km, 6 km
- D. 16 km, 14 km
- Correct Answer
- 8 km, 6 km
ExplanationLet the speed of first lady be (v + 2)km/h and speed of second lady will be v km/h.
Total distance = 24 km
For first lady, Speed = Distance/Time
v + 2 = 24/t ...(i)
Let time taken by first lady to cover distance of 24 km be t h.
Then, time taken by second lady to cover same distance will be(t + 1)h.
For second lady, Speed =Distance/time
v = 24/(t + 1) ...(ii)
Form Eqs.(i) and (ii), we get
24/t - 2 = 24/(t + 1)
? (24 - 2t)/t = 24/(t + 1)
? (24 - 2t)(t + 1) = 24t
? 24t - 2t2 + 24 - 2t = 24t
? 2t2 + 2t - 24 = 0
? t2 + t - 12 = 0
? t2 + 4t - 3t - 12 = 0
? t(t + 4) -3(t + 4) = 0
? (t - 3)(t + 4) = 0
? t = 3, -4
? t = 3 (t ?- 4)
? The distance travelled by the first lady in one hour
= 24/t = 24/3 = 8 km
And distance travelled by the second lady in one hour
= 24/t + 1
= 24/3 + 1 = 6 km
- 1. Two cars A and B start simultaneously from a certain place at the speed of 30 km/h and 45 km/h, respectively.The car B reaches the destination 2 h earlier than A. What is the distance between the starting point and destination?
Options- A. 90 km
- B. 180 km
- C. 270 km
- D. 360 km Discuss
- 2. A train runs for 3 h at the speed of 40 km/h and then for 4 1/ 2 h at the speed of 60 km/h. Thus, it covers 3/5th part of the whole distance. It wants to cover the remaining distance in 4 h, find the average speed of the train for remaining distance?
Options- A. 45 km/h
- B. 35 km/h
- C. 80 km/h
- D. 65 km/h Discuss
- 3. A and B are two station 1000 km apart. A train starts from A and moves towards B at 40 km/h. Another train starts from B at the same time and moves towards A at 60 km/h. How far from A will they cross each other?
Options- A. 350 km
- B. 400 km
- C. 525 km
- D. 300 km Discuss
- 4. A car runs at the speed of 50 km/h when not serviced and runs at 60 km/h, when serviced. After servicing, the car covers a certain distance in 6 h. How much time will the car take to cover the same distance when serviced?
Options- A. 8.2 h
- B. 6.5 h
- C. 8 h
- D. 7.2 h Discuss
- 5. A car travels a distance of 75 km at the speed of 25 km/h. It covers the next 25 km of its journey at the speed of 5 km/h and the last 50 km of its journey at the speed of 25 km/h. What is the average speed of the car?
Options- A. 40 km/h
- B. 25 km/h
- C. 15 km/h
- D. 12.5 km/h Discuss
- 6. A train runs with a speed of 200 km/hour. What will be its speed in m/sec?
Options- A. 50 m/sec
- B. 55.55 m/sec
- C. 48 m/sec
- D. 66.66 m/sec Discuss
- 7. A train crosses a pole in 10 sec and a 200m long platform in 20 sec. What is the length of the train?
Options- A. 100m
- B. 200m
- C. 250m
- D. 300m Discuss
- 8. Two trains running at 36 km/hr and 54 km/hr are running parallel in the opposite direction. If their lengths are 200m and 300m respectively. Then how much time will they take to cross each other?
Options- A. 20 sec
- B. 25 sec
- C. 30 sec
- D. 35 sec Discuss
- 9. A 200 m long train is running at a speed of 60 km/ hr. Find out the time it takes to pass a man standing at the platform
Options- A. 10 sec
- B. 12 sec
- C. 15 sec
- D. 18 sec Discuss
- 10. A train is running at the speed of 264 Km/hr. If the length of the train is 330m, then how long will it take to cross a platform which is 330m long?
Options- A. 9 sec
- B. 11 sec
- C. 12 sec
- D. 15 sec Discuss
Time and Distance problems
Search Results
Correct Answer: 180 km
Explanation:
Let the time taken by car B to reach destination is T h.
So, the time taken by car A to reach destination is (T + 2) h.
Now, S1T1 = S2T2
? 30(T + 2) = 45 x T
? 30T + 60 = 45T
? 15T = 60
? T = 4 h
Now, distance between starting point and destination = S2T2
= 45 x 4 = 180 km
Correct Answer: 65 km/h
Explanation:
Let total distance = D
Now, according to the question,
40 x 3 + 60 x 4.5 = 3D/5
? 120 + 270 = 3D/5
? D = 390 x 5/3 = 650 km
? Remaining distance = [650 - (3/5) x 650]
= 650 - 390 = 260 km
Required average speed = 260/4 = 65 km/h
Correct Answer: 400 km
Explanation:
Let they meet x km from A.
Then, according to the question,
x/40 = (1000 - x)/60
? 60 x = 40(1000 - x)
? 3x = 2000 - 2x
? 3x + 2x = 2000
? 5x = 2000 km
? x = 2000/5 = 400 km
Correct Answer: 7.2 h
Explanation:
After sevicing speed of car = 60 km/h
? Distance covered in 6 h = 60 x 6 km = 360 km.
When not serviced, then time taken to cover 360 km = 360/50 = 7.2 h
Correct Answer: 15 km/h
Explanation:
Time taken to cover first 75 km = 75/25 = 3 h
Time taken to cover next 25 km = 25/5 = 5 h
Time taken to cover last 50 km of its journey = 50/25 = 2 h
Total distance = 75 + 25 + 50 = 150 km
Total time taken = 3 + 5 + 2 = 10 h
? Required average speed = Total distance / Total time taken
= 150/10 = 15 km/h
Correct Answer: 55.55 m/sec
Explanation:
Speed in km/ hour =200
Speed in m/sec = 200 x 5/18 = 500/9 m/sec = 55.55 m/sec
Correct Answer: 200m
Explanation:
Let the length of train be x meter and speed be y m/sec
Therefore, time taken to cross the pole = x/y sec
and time taken to cross the platform = ( Length of train + Length of platform) / speed of train
Therefore x/y = 10
And, (x+200) / y = 20
? 10y + 200 = 20 y
? speed of train, y = 20 m/sec
And length of rain = x = 10y = 200m
Correct Answer: 20 sec
Explanation:
Relative speed, when the trains are running in the opposite direction = Sum of the speed
Therefore, Relative speed = 36 km/hr +72 km/hr = 90 km/hr
Relative speed in m/sec = 90 km/hr x 5/18= 25 m/sec
Distance covered = sum of the lengths of the train = 200 m+ 300 m = 500m
Therefore, time taken = 500m / 25 m/sec = 20 sec
Correct Answer: 12 sec
Explanation:
Speed of the train = (60 x 5/18) m/sec = 50/3 m/sec
Distance covered in passing the standing person = 200m
Required time taken= =200/(50/3) = 200 x (3/50) = 12 sec
Correct Answer: 9 sec
Explanation:
Speed of the train = (264 x 5/18) m/sec = 220/3 m/sec
Distance covered in passing the platform = (330+330) m= 660m
Time taken= ( 660 / (220/3) ) sec = (660 x 3/ 220 ) = 9 sec
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