Aptitude - Problems on Trains - Discussion
Discussion Forum : Problems on Trains - General Questions (Q.No. 28)
28.
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?
Answer: Option
Explanation:
| 4.5 km/hr = |  |
4.5 x | 5 |  |
m/sec = | 5 | m/sec = 1.25 m/sec, and |
| 18 | 4 |
| 5.4 km/hr = | |
5.4 x | 5 | |
m/sec = | 3 | m/sec = 1.5 m/sec. |
| 18 | 2 |
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
 Speed of the train = |
|
22.5 x | 18 | |
km/hr = 81 km/hr. |
| 5 |
Discussion:
54 comments Page 4 of 6.
Kavi said:
9 years ago
In the answer, x is distance because speed * time, how come you say that x is speed?
Sathees said:
9 years ago
Let be considered x is a length, y is a speed, p1 and p2 both represent the person.
Step 1 : p1, p2 speed given for km/hr, Time is given for seconds so km/hr convert to m/s.
P1 => 4.5 * 5/18 = 1.25 m/sec and,
p2 => 5.4 * 5/18 = 1.5 m/sec.
Step 2 : Length or distance (m) = (train speed - person speed) m/sec * time.
x = (y - 1.25) * 8.4,
=> x = 8.4 y - 10.5,
=> 8.4 y - x = 10.5,
x = (y - 1.5) * 8. 5,
=> x = 8.5 y - 12.75,
=> 8. 5 y - x = 12.75.
Step 3:
8.5 y - x = 12.75
8.4 y - x = 10.5
----------------------
0.1 y = 2.25
----------------------
=> y = 22.5 m/sec.
Step 4 : m/sec convert into km/hr (ans is given for km /hr).
y = 22.5 * 5/18
= 4.5 * 18
= 81.0 km/hr.
Step 1 : p1, p2 speed given for km/hr, Time is given for seconds so km/hr convert to m/s.
P1 => 4.5 * 5/18 = 1.25 m/sec and,
p2 => 5.4 * 5/18 = 1.5 m/sec.
Step 2 : Length or distance (m) = (train speed - person speed) m/sec * time.
x = (y - 1.25) * 8.4,
=> x = 8.4 y - 10.5,
=> 8.4 y - x = 10.5,
x = (y - 1.5) * 8. 5,
=> x = 8.5 y - 12.75,
=> 8. 5 y - x = 12.75.
Step 3:
8.5 y - x = 12.75
8.4 y - x = 10.5
----------------------
0.1 y = 2.25
----------------------
=> y = 22.5 m/sec.
Step 4 : m/sec convert into km/hr (ans is given for km /hr).
y = 22.5 * 5/18
= 4.5 * 18
= 81.0 km/hr.
(2)
Varun said:
8 years ago
Thank you @Sathees.
Aktar said:
8 years ago
Let the speed of train be x m/s, & the distance be y m; here, 4.5km/hr = 1.25m/s and 5.4km/hr=1.5m/s.
Aaccording to question, y/(x-1.25)=8.4, y=8.4x-10.5 ----(i)
Again, y/(x-1.5)=5.4, y=5.4x-8.1 ----(ii)
Solving (i) & (ii), x =22.5 Ans: 22.5 m/s.
Aaccording to question, y/(x-1.25)=8.4, y=8.4x-10.5 ----(i)
Again, y/(x-1.5)=5.4, y=5.4x-8.1 ----(ii)
Solving (i) & (ii), x =22.5 Ans: 22.5 m/s.
(1)
Priyanka said:
8 years ago
Why equating both distances?
Please explain me.
Please explain me.
Pooja said:
8 years ago
Nice explanation, Thanks @Sathees.
Mpa said:
8 years ago
How does distance can be equal?
San said:
8 years ago
How distance and speed are equal here?
PrasannKumar said:
8 years ago
@Priyanka.
Both are the distances of the train only to get the answer he equated.
Both are the distances of the train only to get the answer he equated.
Swapnil said:
7 years ago
Both equations is equated because, distance cover by train for both the person is same, ie. Length of the train.
So in solution calculate the distance cover by train (length of the train) for both the person from given data and then equated them. Because distance covered by train (length of the train) is same for both the person.
So in solution calculate the distance cover by train (length of the train) for both the person from given data and then equated them. Because distance covered by train (length of the train) is same for both the person.
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