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19 Oct 2017, 11:12
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
58% (03:41) correct
42%
(03:34)
wrong
based on 316
sessions
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A train X departs from station A at 11.00 am for station B, which is 180 km away. Another train Y departs from station B at 11.00 am for station A. Train X travels at an average speed of 70 kms/hr and does not stop any where until it arrives at station B. Train Y travels at an average speed of 50 kms/hr, but has to stop for 15 minutes at station C, which is 60 kms away from station B en route to station A. Ignoring the lengths the train, what is the distance, to the nearest km, from station A to the point where the trains cross each other?
A. 112
B. 118
C. 120
D. 122
E. Cant be determined
A. 112
B. 118
C. 120
D. 122
E. Cant be determined
19 Oct 2017, 13:06
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anupamdev
Time taken by train Y to travel a distance of 60km\(= \frac{60}{50}*60=72\) minutes
Train Y was stationed at point C for 15 minutes, hence total time elapsed to reach point C \(= 72+15=87\) minutes.
During this period train X covered a distance of \(= 70*\frac{87}{60} = 101.5\) or approx \(102\)km
so distance left between these two train to cover \(= 180-102-60=18\)km
as the trains are moving in opposite direction, relative speed \(= 70+50=120\) km/h
time taken to cover 18km \(= \frac{18}{120}\)
so distance traveled by train X \(= 70*\frac{18}{120}=10.5\)
Hence train X's distance from A \(= 102+10.5=112.5 =112\) (as rounding was done earlier)
Option A
Quickest method: Assume X runs for 't' hrs. to meet Y. Then Y runs for (t-1/4)hrs. to meet X (since Y makes a 15 min. stopover). So, in order to arrive at the meeting point, distance covered by A is 70t kms and that covered by Y is 50(t-1/5). The sum of these two distances is the distance between Stations A & B which is 180kms. So, 180=70t+50(t-1/4). Thus, t=(77/48)hrs. The distance of the meeting point from Station A is the distance traveled by X which is 70(77/48)=112.3
Note: The fact that Station C is 60kms from B is irrelevant. In fact, C could have been anywhere along the route as long as it was less than (180-112.3)kms from Station B.
Note: The fact that Station C is 60kms from B is irrelevant. In fact, C could have been anywhere along the route as long as it was less than (180-112.3)kms from Station B.
