A farmer has decided to build a wire fence along one straight side of his 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?
Answer: D
Let the number of posts to be bought be n.
The length of the side of the property, when posts are at 6 meters distance = 6(n − 1) …(i)
The length of the side of the property, when posts are at 8 meters distance = 8(n − 5− 1) …(ii)
From (i) and (ii),
∴ 6(n − 1) = 8(n − 5− 1)
Solving this, we get n = 21
∴ Length of property = 6(21 − 1) = 120
∴ Number of posts the farmer bought = 21 − 5 = 16
Hence, option (d).