Zeeshan has a faulty compass which shows North as South-West, East as North-West and so on. If Zeeshan wants to actually find the South-East direction on his compass, then he should check which direction on his compass so that he gets to determine the South-East direction correctly?

1. Understand the Defect:

• When facing Actual North ($0^\circ$), the compass reads South-West ($225^\circ$).
• The shift from Actual to Compass reading is a rotation of $+225^\circ$ clockwise ($0^\circ + 225^\circ = 225^\circ$).
• Let's verify with East: When facing Actual East ($90^\circ$), the compass reads North-West ($315^\circ$). This matches perfectly ($90^\circ + 225^\circ = 315^\circ$).

2. Apply to the Goal:

• Zeeshan wants to move in the Actual South-East ($135^\circ$) direction.
• To find out what his broken compass will read when he points himself South-East, apply the exact same $+225^\circ$ clockwise shift:

$\text{Compass Reading} = 135^\circ \text{ (Actual)} + 225^\circ = 360^\circ \text{ or } 0^\circ$

• $0^\circ$ (or $360^\circ$) is North.

Therefore, if Zeeshan aligns himself so that his faulty compass needle points to North, he will actually be heading South-East.

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Recommended Corrected Solution Text

The correct option is Option 4: North.

Detailed Explanation:

Let's track the clockwise angle rotation from true geographic directions to what Zeeshan's faulty compass displays ($0^\circ = \text{North}$, $90^\circ = \text{East}$, $180^\circ = \text{South}$, $270^\circ = \text{West}$):

• Actual North ($0^\circ$) is displayed as South-West ($225^\circ$).

$\text{Shift} = 225^\circ - 0^\circ = +225^\circ \text{ clockwise.}$

• Actual East ($90^\circ$) is displayed as North-West ($315^\circ$).

$\text{Shift} = 315^\circ - 90^\circ = +225^\circ \text{ clockwise.}$

The faulty compass consistently shifts every true direction by adding $+225^\circ$ clockwise.

To find out what direction he needs to follow on his faulty dial to head in the Actual South-East ($135^\circ$) direction, apply the same constant shift:

$\text{Compass Display} = \text{Actual Direction} + 225^\circ$

$\text{Compass Display} = 135^\circ + 225^\circ = 360^\circ \text{ (which is } 0^\circ\text{)}$

Since $0^\circ / 360^\circ$ corresponds to North, Zeeshan must look for North on his faulty compass dial to correctly navigate South-East.