A country has the following types of traffic signals:
• 3 red lights = stop
• 2 red lights = turn left
• 1 red light = turn right
• 3 green lights = go at 100 km/hr speed
• 2 green lights = go at 40 km/hr speed
• 1 green light = go at 20 km/hr speed
A motorist starts at a point on a road and follows all traffic signals. His car is heading towards the north. He encounters the following signals (the time mentioned in each case below is applicable after crossing the previous signal).
• Starting point- 1 green light
• After half an hour, 1st signal- 2 red and 2 green lights
• After 15 min, 2nd signal- 1 red light
• After half an hour, 3rd signal- 1 red and 3 green lights
• After 24 min, 4th signal- 2 red and 2 green lights
• After 15 min, 5th signal- 3 red lights
The total distance travelled by the motorist from the starting point till the last signal is
Show Hint
- 90 km
- 100 km
- 120 km
- None of these
The Correct Option is B
Solution and Explanation
- Starting point: 1 green light → speed = 20 km/hr, time = 0 min.
- After 30 minutes (1st signal): 2 red and 2 green lights → speed = 40 km/hr for 30 minutes = 20 km.
- After 15 minutes (2nd signal): 1 red light → speed = 0 km/hr for 15 minutes = 0 km.
- After 30 minutes (3rd signal): 1 red and 3 green lights → speed = 100 km/hr for 30 minutes = 50 km.
- After 24 minutes (4th signal): 2 red and 2 green lights → speed = 40 km/hr for 24 minutes = 16 km.
- After 15 minutes (5th signal): 3 red lights → speed = 0 km/hr for 15 minutes = 0 km.
Adding up all the distances gives: \[ 20 + 0 + 50 + 16 + 0 = 100 \, \text{km} \] Thus, the total distance travelled is 100 km. \[ \boxed{100 \, \text{km}} \]
What is the position (radial distance) of the motorist when he reaches the last signal?
Show Hint
- 45 km directly north of the starting point
- 30 km directly to the east of the starting point
- 50 km away to the north-east of the starting point
- 45 km away to the north-west of the starting point
The Correct Option is C
Solution and Explanation
- After the first signal, the motorist moves 20 km to the north.
- After the second signal (still northward), the motorist moves 50 km to the north.
- After the fourth signal, the motorist turns to the east and travels 16 km.
Using Pythagoras’ theorem to calculate the resultant position from the starting point: \[ \text{Radial distance} = \sqrt{(50^2 + 16^2)} = \sqrt{2500 + 256} = \sqrt{2756} \approx 52.5 \, \text{km}. \] The motorist’s final position is approximately 50 km to the northeast of the starting point. \[ \boxed{50 \, \text{km north-east}} \]
After the starting point, if the 1st signal were 1 red and 2 green lights, what would be the final position of the motorist?
Show Hint
- 30 km to the west and 20 km to the south
- 30 km to the west and 40 km to the north
- 50 km to the east and 40 km to the north
- Directly 30 km to the east
The Correct Option is B
Solution and Explanation
If at the starting point, the car was heading towards south, what would be the final position of the motorist?
Show Hint
- 30 km to the east and 40 km to the south
- 30 km to the west and 40 km to the south
- 50 km to the east and 40 km to the south
- 50 km to the west and 20 km to the north
The Correct Option is C
Solution and Explanation
- After the next few signals, the motorist turns east and moves 16 km.
- Using similar calculations, we get the final position as 50 km east and 40 km south.
\[ \boxed{50 \, \text{km east and 40 km south}} \]
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