A train approaches a tunnel AB.
Inside the tunnel is a cat located at a point that is 3/8 of the distance AB
measured from the entrance A. When the train whistles the cat runs. If the cat
moves to the entrance of the tunnel A, the train catches the cat exactly at the
entrance. If the cat moves to the exit B, the train catches the cat at exactly
the exit. The speed of the train is greater than the speed of the cat by what
order?
(a) 3:1
(b) 4:1
(c) 5:1
(d) None of these

Let
the length of the tunnel be x and distance of the train to entrance A be y. Let
the speeds of train and cat bet and c respectively.
Hence, when the cat runs 3x/8, the train covers
y.
=>(3x/8)/c=y/t---(1)
When the cat runs 5x/8 to the other end, the train covers x+y
=>(5x/8)/c = (x+y)/t
(2)
Taking ratio of (1) to (2)
3/5=y/(x+y)=>3x
= 2y---(3)
Substituting (3) in (1)
(2y/8)/c=y/t
=> t = 4c
Hence the ratio t:c is 4:1.