Two friends X and Y start running and they run together for 50 m in the same direction and reach a point. X turns right and runs 60 m, while Y turns left and runs 40 m. Then X turns left and runs 50 m and stops, while Y turns right and runs 50 m and then stops. How far are the two friends from each other now?

The correct option is 100 m.

Let us break down the movements of both friends step-by-step to determine their final positions relative to each other.

Step 1: Initial joint movement
Both X and Y start at the same point (let's call it the starting point, O) and run together for 50 m in the same direction. Let's assume they run east. They reach Point A, which is 50 m east of Point O.

Step 2: X's movements
From Point A, X turns right (which would be south, if they were heading east) and runs 60 m. Let's call this Point B.
Then, X turns left (which is east, since X was facing south) and runs 50 m to stop at Point C.
So, relative to Point A, X's final position is 60 m south and 50 m east.

Step 3: Y's movements
From Point A, Y turns left (which would be north, if they were heading east) and runs 40 m. Let's call this Point D.
Then, Y turns right (which is east, since Y was facing north) and runs 50 m to stop at Point E.
So, relative to Point A, Y's final position is 40 m north and 50 m east.

Step 4: Finding the distance between X and Y
Both X (at Point C) and Y (at Point E) have traveled an equal distance of 50 m east from Point A's vertical line. This means they are on the same vertical line, 50 m east of Point A.
Since their horizontal coordinates (east-west positions) are the same, the distance between them is simply the vertical distance between X's southern position and Y's northern position relative to Point A.
Distance = (Distance of Y north of A) + (Distance of X south of A)
Distance = 40 m + 60 m = 100 m.

Therefore, the two friends are 100 m apart from each other now.