Question

Speeds of dhoni and sachin were 8 km/hr and 5 km/hr, then after what time will the two meet for the first time at the starting point if they start simultaneously? The length of the circular track is 500 m.

Answer 1

time taken by Dhoni to complete one revolution =
$\frac{500}{8} \times \frac{18}{5} = 225 \: sec$
similarly, time taken by Sachin to complete one revolution =
$\frac{500}{5} \times \frac{18}{5} = 360 \: sec$
after completing one revolution by Dhoni,

d = distance to travel by Dhoni to catch Sachin
= distance traveled by Sachin in 225 sec
= 225 x 5 x 5 / 18
= 225 x 25 / 18 m

v = relative speed of Dhoni wrt Sachin = (8 - 5) x 5 / 18 = 5/6 m/s

time taken to catch Sachin by Dhoni = d / v
= (225 x 25 x 6) / ( 18 x 5)

= 375 sec

hence, total time ellapsed to meet first time after start
= 225 + 375
= 600 sec
= 10 min ..... Answer