After an accident a train moves at $\frac{2}{3}$ of its original speed and due to this it reaches 45 minute late. What is the original time of journey?

90 minutes

Let the speed of the train = 3x

After accident it travels with = 2/3 × 3x = 2x

so, if the distance is same then the speed is inversely proportional to the time,

So, Speed = 3x  :  2x

Time will be = 2x  :  3x

So, extra time = 3x - 2x = x

x = 45 min

So, the original time = 45 × 2 = 90min