Question

a theif run with a uniform speed of 10m/minute after 10 minute policeman run after the theif to catch him he goes with speed of 100m/min in first minute and increase his speed by 10m/min every succeeding mintue after how many mintues the policemen will catch theif​

Answer 1

Answer:

5 minutes

Hey guy, your question must be a theif run with a uniform speed of 100m/minute after 10 minute instead of a theif run with a uniform speed of 10m/minute after 10 minute

Step by step explaination:

Let,

the police catch the thief in n min

As the thief ran 1 min before the police

Time taken by the thief before being caught =(n+1) min

Distance travelled by the thief in (n+1) min

=100(n+1)m

Speed of police in 1st min=100m/min

Speed of police in 2nd min=110m/min

Speed of police in3rd min =120m/min. and so on

∴100,110,120,... this forms an AP

Total distance travelled by the police in n min =

n/2 (2×100+(n−1)10)

On catching the thief by police,distance traveled by thief= distance travelled by the police

⇒100(n+1)= n/2 (2×100+(n−1)10)

⇒100n+100=100n+ n/2 (n−1)10

⇒100=n(n−1)5

⇒n²-n-20=0

⇒(n−5)(n+4)=0

⇒n−5=0,n+4=0

⇒n=5 OR n=−4(but this is not possible) because nobody can run in negative speed.

so, n=5

Time taken by the policeman to catch the thief=5min

hope it helps.