A train moving at the same speed passes two bridges of length 900 m and 486 m in 110 seconds and 70 seconds, respectively. The length of the train (in m) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 238.5.
Let the length of the train be L meters and speed be v m/s.
Time = Distance ÷ Speed
For first bridge:
L + 900 = v × 110
For second bridge:
L + 486 = v × 70
Now subtract equations:
(L + 900) − (L + 486) = 110v − 70v
⇒ 900 − 486 = 40v
⇒ 414 = 40v
⇒ v = 414 ÷ 40 = 207 ÷ 20
Now substitute in first equation:
⇒ L + 900 = 110 × 207 ÷ 20
= (110 × 207) ÷ 20
= 22770 ÷ 20
= 11385 ÷ 10
= 1138.5
So, L = 1138.5 − 900 = 238.5