A person covers some part of 270 km journey by plane and rest by train in 5 hours. If he covers total distance by plane in 3 hrs then he saves \(\frac{2}{3}\) rd of the time spend in train. Find the distance (in km) covered by plane.

180

Total distance to be traveled = 270 km

As, By travelling whole distance through plane saves \(\frac{2}{3}\)rd of time taken by train.

So, \(\frac{1}{3}\)rd of time taken by train = 3 hours

Total time taken by train = 9 hours

By using allegation method,

As,

3R = 270 km

1R = 90 km

2R = 2 x 90 = 180 km

So, Distance traveled by 180 km