To catch a Thief.........

Algebra Level 4

In cross examination the lawyer for accused asked the police officer how he could catch up with the accused who was already 36 steps ahead of him, when he started to run after him.

The officer replied: "Yes sir, he takes 3 steps to every 2 of mine."

"But then how did u ever catch him, if that was the case..?" interrogated the lawyer.

"That's easily explained..I have got a longer stride", replied the officer. "2 steps of mine are equal to his 5. So the number of steps I required were fewer than his."

How many steps did the officer take to catch up with the thief..?

(You can assume that the lead of 36 steps were thief-steps)


The answer is 36.

Rohit Sachdeva by Rohit Sachdeva , 30, India

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3 solutions

Rohit Sachdeva
Sep 18, 2014

Let 1 step of Police = P mtr & 1 step of Thief = T mtr

2P = 5T

Now let Police take S steps

Then Thief will take (3S/2) steps

SP = 36T + (3S/2)T

S(5T/2) = 36T + (3S/2)T

S = 36 which is our required answer.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Nikhil Tyagi
Jan 26, 2015

The Steps of the Police officer are 2.5 times steps of the thief for every 3 steps the thief took police officer took 5 steps so for every 1.5 steps of thief the police officer took 2.5 steps(1 step for the police officer). So distance covered after 36 steps(policemen) = (2.5-1.5)*36 = 36 steps(thief)

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Fox To-ong
Feb 13, 2015

First condition: P/2 = T/3 Next condition: P/2 = T+36/(5) P= 36

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