Problem Solving

Hi,

Can someone please help to solve the problem attached.
I am getting answer as 1/3,but OA shows 1/4

Thanks.

Total degree in a semicicrcle in 180

In a Quarter Circle is 90

Now the angle is given as 45 degrees, so the remaining angle too is 45 degrees.

Now the length of arc is 2*pie*angle

For the semicircle it is 2*pie*180 while for the required arc it is 2*pie*45.

The ratio of the two is 1:4 and hence the answer is 1:4