Question

A man is laying stones, from start to end, along the two sides of a 200-meterwalkway. The stones are to be laid 5 meters apart from each other. When he begins, all the stones are present at the start of the walkway. He places the first stone on each side at the walkway’s start. For all the other stones, the man lays the stones first along one of the walkway’s sides, then along the other side in an exactly similar fashion.
However, he can carry only one stone at a time. To lay each stone, the man walks to the spot, lays the stone, and then walks back to pick another. After laying all the stones, the man walks back to the start, which marks the end of his work. What is the total distance that the man walks in executing this work? Assume that the width of the walkway is negligible.

• A. 16400 metres
• B. 4100 metres
• C. 8050 metres
• D. 16200 metres
• E. 8200 metres

Answer 1

The Correct Option is A

The problem involves the man laying stones on both sides of a 200-meter walkway, with stones placed 5 meters apart. He places two stones at the start and continues with the remaining stones alternating between the two sides of the path. 

To calculate the total distance he walks, follow these steps:

1. Calculate the number of stones laid on each side:

Since stones are placed every 5 meters along a 200-meter path, the number of stones required per side is: 200/5+1=41

1. Total stones for both sides:

Multiply by 2 because there are two sides: 41×2=82

1. Calculate the total distance walked:

1. The first stone is placed at the starting point (no walking needed).
2. He walks to place stones from 5m to 200m and returns after each placement.
3. Calculate distances walked:

• For each trip to a position (5m to 200m) on one side, he walks there and back:

lwalk=2(5+10+…+195+200)

Arithmetic sequence sum calculation:Sum=n2(a+l)=402(5+200)=20×205=4100

Total walking distance for one side

2×4100=8200

Finally, after laying down all the stones, the man returns to the start, an additional 200m, adding to: 8200+8200+200=16400 meters walked.