Question:
A farmer has decided to build a wire fence along one straight side of this property. For this, he planned to place several fence-posts at six metre intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was five less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them eight metres apart. What is the length of the side of his property and how many posts did he buy?
A farmer has decided to build a wire fence along one straight side of this property. For this, he planned to place several fence-posts at six metre intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was five less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them eight metres apart. What is the length of the side of his property and how many posts did he buy?
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With posts at both ends, a side of length \( L \) with spacing \( d \) needs \( L/d + 1 \) posts. Equate the number of posts bought under the two spacings.
Updated On: Nov 4, 2026
- 100 metres, 15
- 100 metres, 16
- 120 metres, 15
- 120 metres, 16
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The Correct Option is D
Solution and Explanation
Step 1: Set up.
Let the length be \( L \) metres and the posts bought be \( n \).
With 6 m spacing, posts required \( = L/6 + 1 \), and \( n = L/6 + 1 - 5 = L/6 - 4 \).
With 8 m spacing, posts needed \( = L/8 + 1 = n \).
Step 2: Equate.
\( \dfrac{L}{6} - 4 = \dfrac{L}{8} + 1 \Rightarrow \dfrac{L}{6} - \dfrac{L}{8} = 5 \Rightarrow \dfrac{L}{24} = 5 \Rightarrow L = 120 \).
Step 3: Posts bought.
\( n = 120/8 + 1 = 16 \).
Step 4: Check.
6 m spacing needs \( 120/6 + 1 = 21 \) posts, and \( 21 - 5 = 16 \). Correct.
Final Answer:
The correct option is (4): 120 metres, 16
Let the length be \( L \) metres and the posts bought be \( n \).
With 6 m spacing, posts required \( = L/6 + 1 \), and \( n = L/6 + 1 - 5 = L/6 - 4 \).
With 8 m spacing, posts needed \( = L/8 + 1 = n \).
Step 2: Equate.
\( \dfrac{L}{6} - 4 = \dfrac{L}{8} + 1 \Rightarrow \dfrac{L}{6} - \dfrac{L}{8} = 5 \Rightarrow \dfrac{L}{24} = 5 \Rightarrow L = 120 \).
Step 3: Posts bought.
\( n = 120/8 + 1 = 16 \).
Step 4: Check.
6 m spacing needs \( 120/6 + 1 = 21 \) posts, and \( 21 - 5 = 16 \). Correct.
Final Answer:
The correct option is (4): 120 metres, 16
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