Question
A train approaches a tunnel a PQ. Inside the tunnel a
cat located at a point i.e., 7/16 of a distance PQ measured from the entrance P. When the train whistles, the cat runs. If the cat moves to the entrance of the tunnel P, the train catches the cat exactly at the entrance. If the cat moves to the exit Q, 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?Solution
Let the speed of train be ‘a’ and Speed of cat be ‘b’ and Train whistles at a point ‘T’, x km away from P, then First case: => a/b = x/(7k) Second case: => a/b = (x+16)/(9k) From both cases: => 9x = 7 (x+ 16 k) => 9x = 7x = 102 k => 2x = 102k => x/k = 56/1 => a/b = 56/(7x1) = 8/1
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