Atharv starts from Point A and drives 12 km towards west. He then takes a right turn, drives 3 km, turns right and drives 16 km. He then takes a right turn and drives 9 km. He takes a final right turn, drives 4 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 degree turns only unless specified.)
To solve the problem, we will track the journey step-by-step and calculate the final position relative to the starting point, Point A.
- Atharv starts from Point A, driving 12 km towards the west. His current position is 12 km west of Point A.
- He then takes a right turn and drives 3 km. A right turn from west points north, thus he is now 3 km north from the last position.
- He turns right again and drives 16 km. A right turn from north faces east, so he drives 16 km east.
- He makes another right turn and drives 9 km. This turn takes him south, and he drives 9 km.
- Finally, he turns right and drives 4 km. This last right turn points him west.
Now, let's summarize the distances north-south and east-west:
- East-West direction: \(12 \text{ km west} - 16 \text{ km east} + 4 \text{ km west} = 0 \text{ km}\) (He returns to the original east-west line).
- North-South direction: \(3 \text{ km north} - 9 \text{ km south} = -6 \text{ km}\)
The net effect is that Atharv is 6 km south of Point A, because of the overall southward travel.
Therefore, to return to Point A, Atharv should travel 6 km to the north.
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?
