A square park PQRS of side 90 m is so located that its diagonal PR is from north to south and the corner Q is to the west of S. Radha and Mohan start walking along the sides from Q and R respectively in clockwise and anti-clockwise directions with speeds of 8 km/hr and 10km/hr .
Where will they cross each other the second time ?

A distance of 270 m separates Radha and Mohan. Thus, applying the relative motion concept to get the time taken for meeting

$$t=\dfrac{270}{18\times\frac{5}{18}}=54$$ seconds    [Multiplying by 5/18 as we are converting from kmph to m/s]. 

Distance travelled by Radha in 54 seconds =  $$8\times\dfrac{5}{18}\times54=120\ m$$

Thus, Radha and Mohan will meet on PS at a distance of 30 m from P. 

For the second meet, both Radha and Mohan will cover a distance of 360 m. Thus, the time taken to meet again will be -

$$t=\dfrac{360}{18\times\frac{5}{18}}=72$$ seconds

Distance travelled by Radha in next 72 seconds = $$8\times\dfrac{5}{18}\times72=160\ m$$

Thus, Radha's position will be 10 m from R (Continuing on PS for 60 m + SR of 90 m + 10m on RQ)

Thus, they will meet on QR at a 10 m distance from R.