Question

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?

• A. 100 metres, 15
• B. 100 metres, 16
• C. 120 metres, 15
• D. 120 metres, 16

Answer 1

The correct option is D 120 metres, 16

Let the length of the field be X m and let the number of fences he get be Y. Then as per the plan if the farmer tries to arrange them at a distance of 6m each, then there shall be 5 short. Also if he tries to place them 8m apart, then the number of fences required shall be perfectly matching the number available. Hence the equations shall look like: $\left(\frac{X}{6}\right)+1=Y+5;\frac{X}{8}+1=$ Y. Solving Y = 16, also the value of X = 120m.