Arpan starts from Point A and drives 12 km towards East. He then takes a right turn, drives 8 km, turns right and drives 14 km. He then takes a right turn and drives 12 km. He takes a final right turn, drives 2 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only, unless specified)
To find the shortest distance and direction back to Point A, let's track Arpan's movement step-by-step using a coordinate system, starting Point A at $(0, 0)$.
Tracking Arpan's Path
Starts at Point A (0, 0).
Drives 12 km East: Moves to $(12, 0)$.
Turns Right (South) and drives 8 km: Moves to $(12, -8)$.
Turns Right (West) and drives 14 km: Moves to $(-2, -8)$.
Turns Right (North) and drives 12 km: Moves to $(-2, 4)$.
Turns Right (East) and drives 2 km: Moves to $(0, 4)$. This is Point P.
Calculating the Return Trip
Arpan is currently at Point P $(0, 4)$ and needs to get back to Point A $(0, 0)$.
Distance: The difference in the y-coordinates is $4 - 0 = 4$ km.
Direction: Since Point A $(0, 0)$ is directly below Point P $(0, 4)$ on the vertical axis, he needs to drive South.
Conclusion
To reach Point A from Point P, Arpan must drive:
4 km to the south
Important Questions from Direction and Distance
Sita took an auto from her home in Andheri (A) to go to her college in Fatehpuri (F). Rather than continuing straight on the direct road to the college that had no turns, the auto driver took a diversion after 10 km and tumed right at Bandra (B) crossing, then at Colaba T- point (C) after 8 km turned left, again after covering 12 km turned left at Dalhousi Building (D) and soon after 8 km turned right at Elphinston point (E) and after covering 4 km reached Fatehpuri (F). Had the auto driver taken the direct route how much less distance would Sita have actually travelled between the starting point and the destination?
Radha walks a distance of 9 m towards the South-East. Then she walks 15 m towards the West. From here, she walks 9 m towards the North-West. Finally she walks 6 m towards the East and stands at the point. How far is she standing from the starting point?
According to the time by Nihaal's watch its half past one and the hour hand is pointing towards the north-east. Assuming that there is no change in Nihaal's position, in which direction would the minute hand point after 30 minutes?
According to the time by Rohan's watch, it is half past 6 and the watch's hands are pointing to the south. In which of the given directions will the minute-hand point AFTER exactly 24 hours?
According to the time by Rick's watch its quarter past eight. If the minute hand points towards the east, towards which direction would the hour hand point?
