Quantitative Aptitude

Step 1: Understanding the Concept:
Average speed is calculated as the total distance traveled divided by the total time taken. It is not the simple arithmetic average of the speeds.
Step 2: Key Formula or Approach:
Where Total Time is the sum of the time taken for each stretch, and .
Step 3: Detailed Explanation:
The car travels 4 stretches, each of 3 km.
Total Distance = .
Now, let's calculate the time taken for each stretch:
- Time for 1st stretch ( ) =
- Time for 2nd stretch ( ) =
- Time for 3rd stretch ( ) =
- Time for 4th stretch ( ) =
Total Time =
Find a common denominator, which is 60:
hours = 0.6 hours.
Now, calculate the average speed:
Step 4: Final Answer:
The average speed of the car for the entire journey is 20 kmph.

Step 1: Understanding the Concept:
To find the time when the traffic lights will change simultaneously again, we need to find the least common multiple (LCM) of their individual time intervals. The LCM gives the smallest amount of time after which all events will coincide.
Step 2: Key Formula or Approach:
Calculate the LCM of 48, 72, and 108.
Step 3: Detailed Explanation:
First, find the prime factorization of each number:
The LCM is the product of the highest power of each prime factor present in the numbers.
This means the lights will change together every 432 seconds.
Now, convert 432 seconds into minutes and seconds:
So, 432 seconds = 7 minutes and 12 seconds.
The initial simultaneous change was at 8:20:00 hours.
The next simultaneous change will be after 7 minutes and 12 seconds.
New time = 8 hours : 20 minutes : 00 seconds + 7 minutes : 12 seconds
New time = 8:27:12 hours.
Step 4: Final Answer:
The traffic lights will again change simultaneously at 8:27:12 hours.