One morning, after walking a few metres eastward from his house, Harish took three successive left tums walking 180 m, 170 m and 300 m in succession. Finally, he turned right and walked 200 m to reach the temple, which is towards the south-west of his house. If the shortest distance between his house and the temple is 150 m, how far did he walk eastward from his house initially?

Let us assume that Harish started walking towards A and then took 3 left turns and 1 right turn to reach T.
Now, AP = BC = 170 m.
We need to find the value of HP. 
We will draw a perpendicular from H on DT. Length of this perpendicular = PD = 120 m and Hypotenuese is HT i.e. 150m.
This gives the length of base i.e. TQ = 90m. 
Thus QD = 200 - 90 = 110m.
HP = QD = 110m.
AH i.e. the initial distance covered = HP + PA = 110 + 170 = 280m.