A truck from a post office is sent to collect post from a plane as per schedule. The plane lands ahead of schedule, therefore its contents are transported by a rickshaw. The rickshaw meets the truck 30 minutes after the arrival of plane, and the post is transferred. The truck returns to the post office 20 minutes early. How early did the plane arrive? (Assume all transactions are instantaneous.)

Correct option is D

Given:

The plane lands ahead of schedule, and the post is transported by a rickshaw.
The rickshaw meets the truck 30 minutes after the plane's arrival.
The truck, after meeting the rickshaw, returns to the post office 20 minutes early compared to its usual schedule.
Solution:

Let:

"T" represent the scheduled round-trip time for the truck to go to the plane and return to the post office.
Since the truck saved 20 minutes by meeting the rickshaw halfway, the total time taken by the truck in this new scenario is "T - 20" minutes.
Step 1: Analyze the Time Saved
If the truck saved a total of 20 minutes, it means it saved 10 minutes on each leg of the journey (going and returning). Therefore, the truck avoided traveling 10 minutes' worth of distance each way because it met the rickshaw partway.

Step 2: Calculate the Early Arrival of the Plane
Since the rickshaw met the truck 30 minutes after the plane landed, this 30 minutes includes the time saved by the truck. Therefore, the early arrival time of the plane is the time it took for the truck to save each leg of travel (10 minutes) plus the 30 minutes after the plane’s landing when the rickshaw met the truck.

So, the plane arrived: 30 minutes + 10 minutes = 40 minutes early.

Answer: The plane arrived 40 minutes early.