Question

A 1 k.m. long wire is held by n poles. If one pole is removed, the length of the gap becomes 12/3m. What is the number of poles initially?
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Answer 1

Question :- A 1 k.m. long wire is held by n poles. If one pole is removed, the length of the gap becomes 12/3m. What is the number of poles initially ?

Solution :-

Given that,

→ Initial Total Number of Poles = n.

As, we know that, a gap is be exist between two poles.

So,

→ n poles has total gaps = (n - 1).

Therefore,

→ Length of Each gap = (Total Length in metre) / (Total gaps) = 1000/(n - 1)

________

Now,

One Pole is Removed . Than, Total Poles Left are (n - 1).

Than,

→ (n - 1) Poles has Total gaps Now = (n - 1) - 1 = (n - 2) .

Therefore,

→ Length of Each gap now = (Total Length in metre) / (New Total gaps) = 1000/(n - 2)

_________

Now, we have given that, Length of the gap becomes 12/3m.

So,

→ 1000/(n - 2) = 12/3

→ 12(n - 2) = 1000 * 3

→ 12n - 24 = 3000

→ 12n = 3024

Dividing both sides by 12,

→ n = 252. (Ans.)

Hence, The number of Poles Initially were 252.