Neeraj is initially facing north. He first turns 45 degrees to his right and walks 25 metres. Then he turns so that he faces the south east direction and walks another 25 metres. From there he walks 25 metres towards the east. In which direction is Neeraj now located from his original starting position?

Introduction / Context:
This problem is a slightly more advanced direction sense question because it uses diagonal movements such as 45 degree turns and movement along the south east direction. Instead of only orthogonal north, south, east and west legs, we have north east and south east components. The objective is to track Neeraj's net displacement and determine the compass direction of his final position relative to where he started.

Given Data / Assumptions:

• Neeraj starts facing north.
• He turns 45 degrees to his right, which makes him face north east, and then walks 25 metres.
• Next he turns so that he faces south east and walks another 25 metres.
• Finally, from that point, he walks 25 metres towards the east.
• We assume ideal directions: north east means 45 degrees between north and east, and south east means 45 degrees between south and east.
• We must find the direction of his final position from his original starting point.

Concept / Approach:
Because diagonal movements are involved, the most systematic approach is to break each displacement into horizontal (east west) and vertical (north south) components. For movements of 25 metres at 45 degrees, the horizontal and vertical components are equal and can be expressed as 25 divided by square root of 2 in magnitude, one positive and one negative depending on the quadrant. After summing the components of all three legs, we can determine whether Neeraj ends up to the east, west, north or south of the starting point and in which quadrant, if any.

Step-by-Step Solution:
Step 1: Choose a coordinate system with the starting point at (0, 0). Let east be positive x and north be positive y. Step 2: After turning 45 degrees right from north, Neeraj faces north east. A 25 metre move in this direction has components: x = 25 divided by square root of 2, y = 25 divided by square root of 2. So after the first leg, his position is approximately (17.68, 17.68). Step 3: He then turns to face south east. This direction has x positive and y negative. A 25 metre move gives components x = 25 divided by square root of 2, y = minus 25 divided by square root of 2. Adding these to the previous coordinates yields (35.36, 0). Step 4: From this point he walks 25 metres directly east. That changes only the x coordinate. His final position becomes (35.36 + 25, 0) which is approximately (60.36, 0). Step 5: The final y coordinate is zero and the final x coordinate is positive. Thus Neeraj is directly to the east of his starting point, with no north or south component.

Verification / Alternative check:
We may also reason qualitatively. The first and second legs are symmetric diagonal moves: one goes north east and the other south east, each 25 metres. Their vertical components cancel because one is northward and the other is equally southward. However, their horizontal components both point eastward and therefore add up. After these two moves, Neeraj is some distance directly to the east of the starting point. The last leg of 25 metres east simply increases this eastward displacement. Therefore he must end up exactly east of his starting position, which matches the coordinate based conclusion.

Why Other Options Are Wrong:

• Option A, North, would require a net positive y component, which we do not have because the north and south components cancel.
• Option B, West, would correspond to a negative x component, but all movements have eastward horizontal components.
• Option D, South, would require a net negative y component, which again is not present after cancellation.
• Option E, South-East, would require both positive x and negative y displacement; however the net vertical displacement is zero.

Common Pitfalls:
The main difficulty in such problems is correctly handling diagonal movements. Students often forget that north east and south east have equal magnitude components in perpendicular directions, and they mistakenly add or subtract distances without decomposition. Another common mistake is to misinterpret the second turn and add both vertical components instead of cancelling them. Using simple vector components or a rough geometric diagram prevents these errors and makes the pattern of cancellation clear.

Final Answer:
Neeraj's final position lies directly to the East of his original starting point.