Question

A thief, after committing a theft runs at a uniform speed of 50 m/minute. After 2 minutes,
a policeman runs to catch him. He goes 60 m in first minute and increases his speed by
5 m/minute every suceeding minute. After how many minutes, the policeman will catch
the thief?
[CBSE 2016)​

Answer 1

After 1 minute,

Thief = 50m

Police= 0m

After 2 minutes,

Thief = 100m

Police= 0m

After 3 minutes,

Thief = 150m

Police= 60m

After 4 minutes,

Thief = 200m

Police= 60+65m = 125m

After 5 minutes,

Thief = 250m

Police= 125+70m = 195m

After 6 minutes,

Thief = 300m

Police= 195+75m = 270m

After 7 minutes,

Thief = 350m

Police= 270+80m = 350m

Hence, thief will be caught after 7 minutee

Hope it helps!!! :)

Answer 2

Answer:

According to the question,

Distance between thief and police after 2 minutes = 100 m

Police starts chasing thief with initial speed of 60 and increasing his speed by 5 m every minute.

Let the police chase the thief for t minutes.

Implies, thief covers total 100 + 50t m

Police runs with following pattern 60,65,70...

This is an Arithmetic Progression with a = 60, d = 5 & number of terms = t

t/2(2×60+(t−1)×5)=50t+100

t×(120+5t−5)=100t+200

5t

2

+15t−200=0

t

2

+3t−40=0

t={−3±

(9+160)}/2

=(−3±13)/2=+5

Implies, police will catch thief in 5 minutes