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Q.

On the annual day, the pupils of one school made the decision to decorate the building by hanging vibrant flags along the main hallway. They need to fix 27 flags spaced every 2 meters. The flag that is in the middle is where the flags are kept. Ruchi was in charge of putting up the flags. Where the flags were kept was where Ruchi kept her books. She was only able to carry one flag at once. Ruchi travels between finishing this task and getting back to her books for


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a

728m

b

729m

c

730m

d

731m 

answer is A.

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Detailed Solution

Given,
Ruchi needs to fix 27 flags spaced every 2 meters.
The series of numbers form an A.P., if the difference between two consecutive terms is the same. So, according to the question,
It is that the total number of flags is 27 so the middlemost flag will be,
m= n+1 2 m= 27+1 2 m=14  
 Question ImageSimilar to how the third flag would be carried and returned, the distance will be,
Question Image.
Similar to how the third flag would be carried and returned, the distance will be,
Question Image.
So, an AP will be formed to cover a distance by Ruchi to fix the thirteenth flag and return, that is, 4+8+12+....13.
The sum of the 13th term,
S n = n 2 2a+ n1 d  
S 13 = 13 2 2 4 + 131 4 S 13 = 13 2 8+48 S 13 =364   .
Therefore, the total distance traveled by Ruchi to fix the flags and return back is,
D=2×364 D=728m  
Thus, the total distance is 728m.
Therefore, the correct option is 1.
 
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