# Verbal Reasoning - Arithmetic Reasoning - Discussion

### Discussion :: Arithmetic Reasoning - Section 1 (Q.No.29)

29.

A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether ?

 [A]. 100 [B]. 104 [C]. 108 [D]. None of these

Explanation:

Since each pole at the corner of the plot is common to its two sides, so we have :

Total number of poles needed = 27 x 4 - 4 = 108 - 4 = 104.

 Bhati said: (Mar 3, 2013) When its clearly written in question that he used 27 fence poles on each side, then it doesn't matters that each corner is common for 2 sides. He can still use 27 poles for each side, as stated in question.

 Roop said: (Aug 24, 2014) Number of poles between two corners = 25. So 25*4 = 100(4 sides). 100+4 = 104(4 corner poles).

 Kurp said: (Apr 21, 2017) @Roop. Why would it be 25 if it clearly states 27?

 Kurp said: (Apr 21, 2017) I don't understand why 4 was subtracted at all. Please anyone explain it.

 Pranshu Yadav said: (May 9, 2017) We have a square plot in each side there are 27 poles. So, 4 poles are common in each side : (27 * 4)-4 =108-4 = 104 poles. Therefore 104 poles are together used.

 Annie said: (May 18, 2018) Why 4 is subtracted? Please explain it.

 Lakshminnarasimha said: (Jul 23, 2018) Total 27 poles. 25 poles are 4 sides=25*4=100. corner side= 2*2=4, So, Total =104.

 Soya said: (May 18, 2019) 27 pole in each side means, the poles in the corner is common for two sides. Thus we subtracted the poles in the corner, i.e, 4 poles.

 Muskan said: (Jul 14, 2019) Why is 4 subtracted? Explain it?

 Aditya said: (Jul 20, 2019) @Prashnu @Soya. They have mentioned that the poles are along the side of the square. They haven't mentioned that there is a pole common to adjacent sides of a square. Why can't we assume that there are 27 poles on one side of a square and no common pole on the corner, then the answer would have been 27*4=108? That's the reason we are asking that why are the 4 poles subtracted?

 Shibaemon said: (Nov 22, 2019) For those asking why 104, here's a simple visualization. See how they share a common fence. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 26 ** 3 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 25 | 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 24 | 5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 23 | 23 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5 | 24 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4 | 25 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 | 26 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ** 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Remember, the fence we are talking about here is NOT the FLAT kind of fence. Let's take 2 sides, let's say Top and Bottom. Both have 27 fence poles. Then let's take Left and Right sides. They only have 25 fence poles remaining (still 27 per side but we won't count the other 2 because we already had them accounted in Top and Bottom sides). That's (27*2)+(25*2) = 104. or (25*4)+4 common corner = 104.

 Unknown said: (Mar 11, 2020) For those who are asking why 4 is subtracted. Answer: 27 poles on each side. It means 4 poles were commonly shared by all sides. By multiplying *4 we are considering those commonly shared poles also. So we are removing 4 poles. It is like saying a car has 8 wheels instead of 4. By considering the front and back sides also. i.e., right side = 2 wheels. Left side = 2 wheels. Front side =2 wheels. Backside = 2 wheels.