Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
- A4 : 3
- B2 : 5
- C5 : 6
- D1 : 3
Solution & Step-by-step Explanation
Let the speeds of the two trains be y
1
and y
2
respectively.
Express the lengths of the trains:
Length of the first train (L
1
) = speed×time=25×y
1
=25y
1
Length of the second train (L
2
) = speed×time=32×y
2
=32y
2
When crossing each other in opposite directions:
The total distance covered is the sum of their lengths, and the relative speed is the sum of their speeds.
Time=
y
1
+y
2
L
1
+L
2
30=
y
1
+y
2
25y
1
+32y
2
Solve for the ratio y
1
:y
2
:
30(y
1
+y
2
)=25y
1
+32y
2
30y
1
+30y
2
=25y
1
+32y
2
30y
1
−25y
1
=32y
2
−30y
2
5y
1
=2y
2
y
2
y
1
=
5
2
Thus, the ratio of their speeds is 2:5.
1
and y
2
respectively.
Express the lengths of the trains:
Length of the first train (L
1
) = speed×time=25×y
1
=25y
1
Length of the second train (L
2
) = speed×time=32×y
2
=32y
2
When crossing each other in opposite directions:
The total distance covered is the sum of their lengths, and the relative speed is the sum of their speeds.
Time=
y
1
+y
2
L
1
+L
2
30=
y
1
+y
2
25y
1
+32y
2
Solve for the ratio y
1
:y
2
:
30(y
1
+y
2
)=25y
1
+32y
2
30y
1
+30y
2
=25y
1
+32y
2
30y
1
−25y
1
=32y
2
−30y
2
5y
1
=2y
2
y
2
y
1
=
5
2
Thus, the ratio of their speeds is 2:5.