Question

2) A fence has to be made. Posts are to be for every 6 m interval. They are at starting and ending point. Person brings some posts and there are 7 posts lacking. If they are 9 m interval the posts are sufficient. How many posts did the persons bring?

Answer 1

Let the number of posts he bought = x

For the interval of 6 m, 7 more posts are required, ie, x + 7.

So total distance = (x+7- 1)*6 = (x+6)*6 = 6x + 36

(Posts are required at both ends of an interval. So number of intervals will be 1 less than the number of posts)

It is given that that number of posts are sufficient if the interval is 9 m.

From that, the total distance = (x -1)*9 = 9x - 9

Now we can equate both the equations corresponding to distance.

ie, 6x + 36 = 9x - 9

3x = 36 + 9 = 45

x = 45/3 = 15

The person bought 15 posts.

Hope it helps.