Aptitude - Problems on Trains - Discussion
Discussion Forum : Problems on Trains - General Questions (Q.No. 2)
2.
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Answer: Option
Explanation:
| Speed of the train relative to man = |  |
125 |  m/sec |
| 10 |
| = | |
25 | m/sec. |
| 2 |
| = | |
25 | x | 18 | km/hr |
| 2 | 5 |
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 
x = 50 km/hr.
Discussion:
478 comments Page 4 of 48.
Bhavesh sharma/ gadgad786 said:
1 decade ago
Why we are multiplying the 18/5 ?
or we can ask that why we are divide ?
The answer is simple. We are converting the 'kilo-meters/hour' value into 'meters/second'.
Let me explain about converting km/hr into m/s in detail.
1 km = 1000 meters.
1 hr = 3600 seconds.
1 km/hr = 1000/3600 m/s
= 10/36 m/s
= 5/18 m/s.
Therefore 1 km/hr = 5/18 m/sec.
Similarly 60 km/hr = 60 x 5/18 m/sec.
You may ask me, why should I convert it from km/hr to m/sec?
or we can ask that why we are divide ?
The answer is simple. We are converting the 'kilo-meters/hour' value into 'meters/second'.
Let me explain about converting km/hr into m/s in detail.
1 km = 1000 meters.
1 hr = 3600 seconds.
1 km/hr = 1000/3600 m/s
= 10/36 m/s
= 5/18 m/s.
Therefore 1 km/hr = 5/18 m/sec.
Similarly 60 km/hr = 60 x 5/18 m/sec.
You may ask me, why should I convert it from km/hr to m/sec?
Rahul said:
2 decades ago
@ankita
when a man moves in the direction of train, the train speed is decreased by his own speed. If he moves in the opposite directon he finds the train speed to be much greater. So when is moving in the same direction his speed must be subtracted from that of train speed. If he moves in the opposite direction to that of train, then his speed must be added to the train speed.
moving in same directon: SUBTRACT
moving in opposite directon: ADD
when a man moves in the direction of train, the train speed is decreased by his own speed. If he moves in the opposite directon he finds the train speed to be much greater. So when is moving in the same direction his speed must be subtracted from that of train speed. If he moves in the opposite direction to that of train, then his speed must be added to the train speed.
moving in same directon: SUBTRACT
moving in opposite directon: ADD
N Ramesh Chandra said:
2 decades ago
Hai Madhu N Swathi,
****When two bodies say x km/hr and y km/hr are moving in the same direction then their relative speed is (x-y) km/hr
****When we want to convert km/hr in to m/s we multiply with 5/18.
*** Let the speed of the train be x kmph
Speed of the train relative to man(x-5)kmph
(x-5)*5/18
now as we know that Distance/speed=time
now,speed is (x-5)*5/18;
distance is 125m;
time is 10 sec;
now u vl get the answer
***********
****When two bodies say x km/hr and y km/hr are moving in the same direction then their relative speed is (x-y) km/hr
****When we want to convert km/hr in to m/s we multiply with 5/18.
*** Let the speed of the train be x kmph
Speed of the train relative to man(x-5)kmph
(x-5)*5/18
now as we know that Distance/speed=time
now,speed is (x-5)*5/18;
distance is 125m;
time is 10 sec;
now u vl get the answer
***********
VIMAL said:
1 decade ago
This is good Question i understand that, some friend disturb for 18/5. its simple its unit for km/hr. let see that1km=1000m & 1hr = 3600 second so 1000/3600 = 5/18 . And see that If we want to small unit convert in to big unit we have to divide & if we want to big unit convert in to small we have to multiply so here they dividing and write 18/5 ok so encourage your self my friend go ahead. VIMAL SONI & DUSHYANT SONI
Amrit Ashu said:
9 years ago
A different approach:
We have been given the running speed of the man i.e 5km/hr converting this into m/Sec we get 1.38 m/sec.
In 10 seconds this man will cover 13.8 m. So now the total distance the train has to cover in 10 seconds is 125 meters(its own length) and 13.8 m which equals 138.8 m. Using speed, time and distance formula we get S= 138.8/10 =13.8m/sec.
Convert this into Km/h we get 49.8 which is approx. 50 km/h.
We have been given the running speed of the man i.e 5km/hr converting this into m/Sec we get 1.38 m/sec.
In 10 seconds this man will cover 13.8 m. So now the total distance the train has to cover in 10 seconds is 125 meters(its own length) and 13.8 m which equals 138.8 m. Using speed, time and distance formula we get S= 138.8/10 =13.8m/sec.
Convert this into Km/h we get 49.8 which is approx. 50 km/h.
Sourabh said:
2 years ago
Given data :
Length Of the Train 125 meters.
Speed of Man = 5 km/hr
Speed of train = ?
Time = 10 sec.
Distance = Time * Velocity (speed).
125 = 10 × v,
V = 125/10,
V = 25/2 M/sec Now Convert it into Km/hr,
V = 25/2 × 18/5,
V = 45 km/hr.
And given In The Question train And Man Is Traveling in Same Direction.
V = Speed of train - Speed Of Man.
45 = Speed of train - 5.
Speed of train = 45+5.
Speed of train = 50 km/hr.
Length Of the Train 125 meters.
Speed of Man = 5 km/hr
Speed of train = ?
Time = 10 sec.
Distance = Time * Velocity (speed).
125 = 10 × v,
V = 125/10,
V = 25/2 M/sec Now Convert it into Km/hr,
V = 25/2 × 18/5,
V = 45 km/hr.
And given In The Question train And Man Is Traveling in Same Direction.
V = Speed of train - Speed Of Man.
45 = Speed of train - 5.
Speed of train = 45+5.
Speed of train = 50 km/hr.
(180)
Bithal Jena said:
4 years ago
Solution:
Time = Distance/Speed.
Length of train=125m.
Speed of the person in the same direction is 5KM/hr i.e 25/18m/sec
the train takes 10 sec to cross i.e our time.
Let take x as the speed of the train.
So according to the above formula.
10 = 125/x-(25/18),
10 = 125 * 18/18x-25.
x = 13 * 18/5 m/sec.
To make it KM/hr we have to multiply it by the help of 18/5.
13*18/5 * 18/5 = 46km/hr.
So ans should be 46.
Time = Distance/Speed.
Length of train=125m.
Speed of the person in the same direction is 5KM/hr i.e 25/18m/sec
the train takes 10 sec to cross i.e our time.
Let take x as the speed of the train.
So according to the above formula.
10 = 125/x-(25/18),
10 = 125 * 18/18x-25.
x = 13 * 18/5 m/sec.
To make it KM/hr we have to multiply it by the help of 18/5.
13*18/5 * 18/5 = 46km/hr.
So ans should be 46.
(3)
Vishal patel said:
1 decade ago
L = Length of a train.
S1 = Speed of train.
S2 = Speed of man.
T = Time taken by train.
*************** Here is simple formula *********************
T = L/(S1 - S2) * (18/5).
************************************************
10 = 125/(S1 - 5) * (18/5).
=> (S1 - 5) = (125/10)*18/5.
=> (S1 - 5) = (25/2)*18/5.
=> (S1 - 5) = 45.
=> S1 = 45 + 5.
Ans : S1(train's speed) = 50 km/h.
S1 = Speed of train.
S2 = Speed of man.
T = Time taken by train.
*************** Here is simple formula *********************
T = L/(S1 - S2) * (18/5).
************************************************
10 = 125/(S1 - 5) * (18/5).
=> (S1 - 5) = (125/10)*18/5.
=> (S1 - 5) = (25/2)*18/5.
=> (S1 - 5) = 45.
=> S1 = 45 + 5.
Ans : S1(train's speed) = 50 km/h.
Nanda said:
1 decade ago
@ Revathi.
What ever the speed we got first 45 km/hr that is not train speed, that is relative speed because it will come by the intervention of the man speed.
Now we have to cal calculate train speed by follows.
Let the speed of the train be x km/hr.
Relative speed(45kms) = x-5(man speed).
Now x = relative speed(45kms) + 5(right side 5 will come to left side).
Finally x(speed of train) = 45+5 = 50.
What ever the speed we got first 45 km/hr that is not train speed, that is relative speed because it will come by the intervention of the man speed.
Now we have to cal calculate train speed by follows.
Let the speed of the train be x km/hr.
Relative speed(45kms) = x-5(man speed).
Now x = relative speed(45kms) + 5(right side 5 will come to left side).
Finally x(speed of train) = 45+5 = 50.
Shreya Parmar said:
8 years ago
Using [a+b] / [u-v] = t.
a = size of train = 125
b = size of man = 0
u = speed of train = ?
v = speed of man = 5km/hr =5*5/18 = 25/18 m/s
t = time by which train crosses the man =10 sec
substitute the values in the formula we have,
[125-0]/[u- 25/18] = 10
further solving we get
250/18 =u; which is in m/s
now convert it into km/h by multiplying LHS with 18/5
we have u =50km/h
which is the right answer.
a = size of train = 125
b = size of man = 0
u = speed of train = ?
v = speed of man = 5km/hr =5*5/18 = 25/18 m/s
t = time by which train crosses the man =10 sec
substitute the values in the formula we have,
[125-0]/[u- 25/18] = 10
further solving we get
250/18 =u; which is in m/s
now convert it into km/h by multiplying LHS with 18/5
we have u =50km/h
which is the right answer.
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