A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?

Explanation: 1. Calculate Net North-South Displacement: * The woman runs 12 km North, then 6 km South. * Net North displacement = 12 km - 6 km = 6 km North. 2. Calculate Net East-West Displacement: * She runs 8 km East. There is no West movement. * Net East displacement = 8 km East. 3. Determine General Direction: * From her starting point, she is 8 km East and 6 km North. This places her in the North-East quadrant. Therefore, the direction will be "North of East". This eliminates options A and C. 4. Calculate the Angle: * Let the angle (theta) be with respect to the East direction. * We can use the tangent function: tan(theta) = (Opposite side) / (Adjacent side) * Opposite side (North displacement) = 6 km * Adjacent side (East displacement) = 8 km * tan(theta) = 6 / 8 = 3 / 4 = 0.75 5. Compare the Angle with 45 degrees: * We know that tan(45°) = 1. * Since tan(theta) = 0.75, which is less than 1, the angle theta must be less than 45°. 6. Combine Direction and Angle: * The direction is North of East, and the angle is less than 45°. * This matches option B: "An angle less than 45° North of East". Final Check of Options: A) An angle less than 45° South of East - Incorrect, as she is North of East. B) An angle less than 45° North of East - Correct, as calculated. C) In angle more than 45° South of East - Incorrect, as she is North of East and the angle is less than 45°. D) An angle more than 45° North of East - Incorrect, as the angle is less than 45°. The final answer is B.