atricle 2

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Arithmetic Aptitude | Problems on Trains 1 - with Explanation


1
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
A.2 : 3
B.4 : 3
C.6 : 7
D.9 : 16
Answer: Option B
Explanation:
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3.


2
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
A.9 a.m.
B.10 a.m.
C.10.30 a.m.
D.11 a.m.
Answer: Option B
Explanation:
Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
=> 45x = 135
=> x = 3.
So, they meet at 10 a.m.


3
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
A.400 m
B.450 m
C.560 m
D.600 m
Answer: Option A
Explanation:
Let the length of the first train be x metres.
Then, the length of the second train is(x(metres.
2
Relative speed = (48 + 42) kmph =(90 x5(m/sec = 25 m/sec.
18
Therefore[x + (x/2)]= 12 or3x= 300     or     x = 200.
252
Therefore Length of first train = 200 m.
Let the length of platform be y metres.
Speed of the first train =(48 x5(m/sec =40m/sec.
183
Therefore (200 + y) x3= 45
40
=> 600 + 3y = 1800
=> y = 400 m.

4
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A.66 km/hr
B.72 km/hr
C.78 km/hr
D.81 km/hr
Answer: Option D
Explanation:
4.5 km/hr =(4.5 x5(m/sec =5m/sec = 1.25 m/sec, and
184
5.4 km/hr =(5.4 x5(m/sec =3m/sec = 1.5 m/sec.
182
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Therefore Speed of the train =(22.5 x18(km/hr = 81 km/hr.

5
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
A.45 m
B.50 m
C.54 m
D.72 m
Answer: Option B
Explanation:
2 kmph =(2 x5(m/sec =5m/sec.
189
4 kmph =(4 x5(m/sec =10m/sec.
189
Let the length of the train be x metres and its speed by y m/sec.
Then,(x(= 9 and(x(= 10.
y -5
9
y -10
9
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
Therefore Length of the train is 50 m.

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