A flyover has three spans whose lengths are in the ratio 2 : 3 : 5. A bus…
2020
A flyover has three spans whose lengths are in the ratio 2 : 3 : 5. A bus whose length is one-fifth of the total length of the flyover takes t seconds to cross the first span. How many seconds does it take to cross the full flyover?
- A.
2t
- B.
5t
- C.
3t
- D.
4t
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
When a vehicle crosses a fixed object such as a bridge or flyover, the distance covered is the fixed object length plus the vehicle length.
At constant speed, time is proportional to this total crossing distance, not to the fixed object length alone.
Application
Let the three span lengths be 2x, 3x, and 5x, so the total flyover length is 10x.
The bus length is one fifth of the total flyover length, so the bus length is 2x.
To cross the first span, the bus covers the first span plus its own length: 2x + 2x = 4x. Since this takes t seconds, its speed is 4x/t.
To cross the full flyover, the bus covers the flyover plus its own length: 10x + 2x = 12x.
The full crossing time is 12x divided by 4x/t, which equals 3t.
Cross-check
The measured first-span crossing distance is 4x, while the full crossing distance is 12x. The ratio 12x : 4x is 3 : 1, so the required time is 3t seconds.