The students of a school decided to beautify the school . . .

Question : The students of a school decided to beautify the school on the annual day by fixing colourful on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 meter. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

Doubt by Vikrant

Solution : 

Total number of flags = 27

Distance between the any two consecutive spots where the flags will be placed = 2 m
All the flags are placed at the middle flag i.e. (27+1)/2 = 14th flag.

Ruchi will start from the central (14th flag) flag
First she will place 13 flags on left side and she will place the remaining 13 flags on the right side one by one. 

Distance covered by her in placing first flag on left = 2(2) = 4m

Distance covered by her in placing first flag on left = 2(2+2) = 8m

Distance covered by her in placing first flag on left = 2(2+2+2) = 12m
and so on

4, 8, 12.  . . 

This is an AP with First Term (a) = 4 and and common difference (d) = 8-4 = 4

Now, total distance covered by here in placing 13 flags on the left
S1=n/2[2a+(n-1)d]
S1=13/2[2(4)+(13-1)(4)]
S1=13/2[8+12(4)]
S1=13/2[8+48]
S1=13/2[56]
S1=13×28
S1=364

Similarly total distance covered by her in placing 13 flags on the right will be 
S2=364

Total distance covered by her in placing all the flags
=S1+S2
=364+364
=728

The maximum distance she travelled carrying a flag will be the distance between the middle flag and the extreme 13th flag
= 2×13
= 26 m