The party of kejriwal walks from gwalior to Bhuvneshwar. They first walk straight for 150km and then turn 45 ddegree towards Varansi and again go straight for 120km how for have they travelled from the initial place

If I understand it correctly, we have a triangle with sides 150 and 120 with an angle of 135° between them. Clear case of the cosine law.

x^2 = 120^2 + 150^2 - 2(120)(150)cos135°
= ...

tell me you got 249.7 km