Along a road lie an odd number of stones placed at intervals of 10 m. These stones have to be assembled around the middle stone. A man carried the job with one of the end stones by carrying them in succession. In carrying all the stones, he covered a distance of 3 km. Then how many stones were there?

To solve the problem, we need to analyze the situation step by step.

Understanding the Setup

We have an odd number of stones placed 10 meters apart along a road. The man starts from one end and carries each stone to the middle stone.

Distance Calculation

The total distance covered by the man is 3 kilometers, which is equal to 3000 meters. Since he carries each stone from one end to the middle, we need to determine how many stones he moved.

Finding the Number of Stones

• Let the number of stones be represented by n.
• The distance from one end stone to the middle stone is calculated as follows:
• The middle stone is the (n + 1) / 2th stone.
• The distance from the first stone to the middle stone is 10 * ((n - 1) / 2) meters.
• Since he carries each stone to the middle, he makes n trips, covering the distance to the middle stone each time.

Setting Up the Equation

The total distance covered can be expressed as:

n * (10 * ((n - 1) / 2)) = 3000

Which simplifies to:

5n(n - 1) = 3000

Solving for n

Dividing both sides by 5 gives:

n(n - 1) = 600

Now, we need to find an odd integer value for n that satisfies this equation.

Finding the Odd Integer

Testing odd integers:

• If n = 25: 25 * 24 = 600 (this works).

Final Answer

Thus, the total number of stones is 25.