Test Level 3: Speed, Time and Distance - CAT MCQ

The difference between times in two cases = 30 minutes
This difference is only due to the reason that train travelled 60 km distance at 2/3 of its original speed.
Let train initially took t minutes to cover 60 km at its original speed.
According to given condition,
(3t/2) - t = 30
t = 60 minutes
i.e the train initially covered 60 kms in 60 minutes
i.e the initial speed of train is 60 kmph.

Let the total distance be 12d m.
So, the car covers a distance of 4d m at a speed of 4 m/s.
Time taken to cover this distance = (4d/4) s = d s
Let the car take a time of 2t s to cover the remaining 8d m.
So, it travels at a speed of 2 m/s for t seconds and at a speed of 6 m/s for the other t seconds.
Thus, we have 2t + 6t = 8d or t = d.
Now, average speed = total distance/total time = 12d/(d + 2t) = 12d/(d + 2d) = 12d/3d = 4 m/s
Hence, answer option 1 is correct.

The time taken by the flight to fly from Chennai to Singapore is 3 hours.
(Actually, it is 12 - 6 = 6 hours according to the local time, but Singapore is 3 hours ahead of Chennai.)
So, to fly from Chennai to New Jersey, it takes 3  4 = 12 hours (because it is 4 times more distant).
So, the flight which takes off at 9 a.m. in Chennai will reach New Jersey at 9 p.m. according to Chennai time. But then, the local time will be 10 a.m. because it is 11 hours behind.

Let us first calculate the time Saurav and Sachin take to cover one full circle.
Time taken by Saurav =  =  = 225 seconds
Time taken by Sachin =  = 360 seconds
Hence, after every 225 seconds, Saurav would be at the starting point and after every 360 seconds, Sachin would be at the starting point. The time when they will be together again at the starting point simultaneously for the first time would be the smallest multiple of both 225 and 360, which is the LCM of 225 and 360.
Hence, they would both be together at the starting point for the first time after (LCM of 225, 360) = 1800 seconds = 0.5 hour.
Thus, every half an hour, they would meet at the starting point.

When the men first meet, they are 720 yards from one end of the track. The combined distance they have travelled must equal the length of the track.
When each man reaches the other end, the combined distance must be twice the length of the track.
On meeting on the return, they must have travelled a total of three times the length of the track.
Since one man has gone 720 yards on the first meeting and when they meet again, he has gone three times as far, he must have travelled 2160 yards.
Since he is 400 yards from where he started, the length of the track must be 2160 - 400 yards = 1760 yards.

Let us assume that Mr. Hanni sits in the train on Monday. So, he is scheduled to reach on Thursday at 11:30 p.m.
When the train starts from Mumbai, the first Slow-Run Express which he crosses is the one which is scheduled to reach Mumbai at 11:30 p.m, that is the same day (Monday). This train started 3 days ago, i.e. on Friday.
Now, on his way, he will cross the trains which started on Saturday, Sunday and Monday, and the trains which started from Bangalore when Mr. Hanni was himself in the train, i.e. the trains started from Bangalore on Tuesday, Wednesday and Thursday.
Thus, Mr. Hanni must have crossed 7 Slow-Run Express trains during his journey.

Time is given in seconds, so speeds should be metre per second.
Speed of the faster train = 72 × 5/18 = 20 m/s
Speed of the slower train = 54 × 5/18 = 15 m/s
Let the length of the trains be x and y m, respectively.
Total distance to be covered = Sum of the lengths of the two trains = x + y
When they move in opposite directions:
Relative speed = Sum of their speeds = 20 + 15 = 35 m/s
Time taken = 24 seconds
Distance = x + y
Distance = Relative Speed × Time
⇒ x + y = 35 × 24 = 840 m
When they move in the same direction:
Time taken = 18 seconds
Here, the faster train passes Mr. Ravi only, so distance is equal to the length of the faster train.
Distance = Length of the faster train
Distance = Relative Speed × Time
⇒ x = 5 × 18 = 90 m
We have, x + y = 840 and x = 90 m
⇒ y = 750 m
So, the length of the slower train is 750 m.

Ram and Shyam run around a circular track.
Ram crosses Shyam in the middle of the 5^th lap, i.e. when Ram has run four and a half laps, he has covered a distance which is 1 lap greater than that covered by Shyam.
Therefore, when Ram runs 9/2 laps, Shyam runs 7/2 laps.
This is the same as saying when Ram runs 9 laps, Shyam runs 7 laps, i.e. in a race that is 9 laps long, Ram can give Shyam a start of 2 laps.
So, if the race is of 3000 metres long track, then Ram can give Shyam a start of (2/9) × 3000 = 666.67 metres.

Given:
Total distance covered = 42 km
River speed = 6 km/hr
Distance covered in both directions = 21 km
According to the question,
Suppose the speed of boat in still water be x km/hr.
Then, Time taken in rowing upstream = Time taken in returning to the same point + 4 hr

Therefore, the speed of the boat in still water is 8.8 km/hr.
Hence, this is the required solution.

Upstream:
Let t be the time taken by the boat to travel from A to B = 6 hours
Let V₁ be the speed of the boat travelling upstream = x
Let V₂ be the speed of the stream = 2 kmph
Distance = 36 km
V₁ - V₂ = 36/6 = 6 kmph
V₁ = 8 kmph
Downstream:
V₁ = 8 kmph
V₂ = 2 kmph
Net speed = V₁ + V₂ = 10 kmph
Distance = 36 km
Time = 36/10 = 3.6 hours