Question

A Thief runs with a uniform speed of hundred metre per minute after 1 minute a policeman runs after that have to catch him he goes with a speed of 10 metre per minute in the first minute and increases his speed by 10 metre per minute every succeeding minute after how many minutes the policeman will catch the thief.​

Answer 1

Let the thief is caught after x minutes.

After x mins, thief would have covered=100x metres

police would have covered=10(1+2+3....x)metres=10*{x/2(1+x)} metres. (According to Carl Gauss formulae)

As the police caught the thief at this distance, so

100x=10*{x/2(1+x)}

=>100x/10=x/2(1+x)

=>10x=x/2+x^2/2

=>10x*2=x+x^2

=>20x=x(x+1)

=>20x/x=x+1

=>20=x+1

=>x=20-1=19

Thus, the thief will be caught after 19 mins