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The distance between two cities P and Q is 300km. A train starts from station P at 10 am with speed 80 km/hr towards Q. Another train starts from Q towards P with speed 40km/hr at 11 am. At what time do they meet?
- a)12.20pm
- b)12.40 pm
- c)12.50 pm
- d)1 pm
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The distance between two cities P and Q is 300km. A train starts from ...
First train starts at 10am so in one hour it covers 80 km in one hour. Now distance b/w P and Q is 220. Suppose at some’ x’ km they meet. So,
x/80 = (220-x)/40
x = 440/3. The time after which they meet = (440/3)/80 = 11/6 i.e = 1hr 50 min.
x/80 = (220-x)/40
x = 440/3. The time after which they meet = (440/3)/80 = 11/6 i.e = 1hr 50 min.
Most Upvoted Answer
The distance between two cities P and Q is 300km. A train starts from ...
Given:
Distance between two cities P and Q = 300km
Speed of train starting from station P towards Q = 80km/hr
Speed of train starting from Q towards P = 40km/hr
Time at which train starts from station P = 10 am
Time at which train starts from station Q = 11 am
To Find:
Time at which both trains will meet
Solution:
Let's assume both trains meet at a distance x from the station P.
So, the distance covered by the first train in x hours = x km
Distance covered by the second train in (x-1) hours = (300-x) km (as it starts 1 hour later than the first train)
As the distance covered by both trains is the same, we can equate the distance covered by both trains.
x = (80/60)x
300 - x = (40/60)(x-1)
Solving the above two equations, we get:
x = 150 km
So, both trains meet at a distance of 150 km from station P.
Now, let's calculate the time taken by the first train to cover 150 km:
Time taken = Distance/Speed = 150/80 = 1.875 hours
Adding this time to the starting time of the first train (10 am), we get the time at which both trains meet:
= 10:00 am + 1.875 hours
= 11:52 am
Therefore, both trains will meet at 11:52 am. But this is the time when both trains cross each other. We need to calculate the actual time when both trains stop at the meeting point.
The first train started at 10 am and reached the meeting point at 11:52 am. So, it traveled for 1.875 hours.
The second train started at 11 am and reached the meeting point at 11:52 am. So, it traveled for 0.867 hours.
Therefore, the actual time when both trains stop at the meeting point is:
= Starting time of the second train (11 am) + time taken by the second train to reach the meeting point (0.867 hours)
= 11:00 am + 0.867 hours
= 11:52 am + 48 minutes
= 12:40 pm
Hence, the correct option is (c) 12:50 pm.
Distance between two cities P and Q = 300km
Speed of train starting from station P towards Q = 80km/hr
Speed of train starting from Q towards P = 40km/hr
Time at which train starts from station P = 10 am
Time at which train starts from station Q = 11 am
To Find:
Time at which both trains will meet
Solution:
Let's assume both trains meet at a distance x from the station P.
So, the distance covered by the first train in x hours = x km
Distance covered by the second train in (x-1) hours = (300-x) km (as it starts 1 hour later than the first train)
As the distance covered by both trains is the same, we can equate the distance covered by both trains.
x = (80/60)x
300 - x = (40/60)(x-1)
Solving the above two equations, we get:
x = 150 km
So, both trains meet at a distance of 150 km from station P.
Now, let's calculate the time taken by the first train to cover 150 km:
Time taken = Distance/Speed = 150/80 = 1.875 hours
Adding this time to the starting time of the first train (10 am), we get the time at which both trains meet:
= 10:00 am + 1.875 hours
= 11:52 am
Therefore, both trains will meet at 11:52 am. But this is the time when both trains cross each other. We need to calculate the actual time when both trains stop at the meeting point.
The first train started at 10 am and reached the meeting point at 11:52 am. So, it traveled for 1.875 hours.
The second train started at 11 am and reached the meeting point at 11:52 am. So, it traveled for 0.867 hours.
Therefore, the actual time when both trains stop at the meeting point is:
= Starting time of the second train (11 am) + time taken by the second train to reach the meeting point (0.867 hours)
= 11:00 am + 0.867 hours
= 11:52 am + 48 minutes
= 12:40 pm
Hence, the correct option is (c) 12:50 pm.
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Community Answer
The distance between two cities P and Q is 300km. A train starts from ...
First train starts at 10am so in one hour it covers 80 km in one hour. Now distance b/w P and Q is 220. Suppose at some’ x’ km they meet. So,
x/80 = (220-x)/40
x = 440/3. The time after which they meet = (440/3)/80 = 11/6 i.e = 1hr 50 min.
x/80 = (220-x)/40
x = 440/3. The time after which they meet = (440/3)/80 = 11/6 i.e = 1hr 50 min.
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