The students of a school decided to beautify the school on the annual day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. 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 she did cover in completing this job and returning back to collect her books ? What is the maximum distance she travelled carrying a flag ?

Explanation

Given that, the students of a school decided to beartify the school on the annual day by fixing colourful flags on the straight passage of the school.
Given that, the number of flags = 27 and distance between each flag =2m.
Also, the flags are stored at the position of the middle most flag i.e., 14th flag and Ruchi was given the responsibility of placing the flags. Ruchi kept her books, where the flags were stored i.e., 14th flag and she could carry only one flag at a time.
Let she placed 13 flags into her left position from middle most flag i.e., 14th flag. For placing second flag and return his initial position distance travelled = 2 + 2=4m.
Similarly, for placing third flag and return his initial position, distance travelled = 4 + 4 = 8m.
For placing fourth flag and return his initial position, distance travelled = 6 + 6 = 12m.
For placing fourteenth flag and return his initial position, distance travelled = 26 + 26 = 52m.
Proceed same manner into her right position from middle most flag i.e., 14th flag.
Total distance travelled in that case = 52m
Also, when Ruchi placed the last flag she return his middle most position and collect her books. This distance also included in placed the last flag.
So, these distances form a series.
`4+8+12+16+ ... +52 " "` [for left]
and `4+8+12+16+ ... +52 " "` [for right]
` :. ` Total distance covered by Ruchi for placing these flags
`=2xx(4+8+12+ ... +52)`
`=2xx[(13)/(2){2xx4+(13-1)xx(8-4)}] " "{( :' "Sum of n terms of an AP")/(S_(n)=(n)/(2)[2a+(n-1)d])}`
`=2xx[(13)/(2)(8+12xx4)] " " ` [` :' ` both sides of Ruchi number of flags i.e., n = 13]
`=2xx[13(4+12xx2)]=2xx13(4+24)`
`=2xx13x28=728m`
Hence, the required is 728 m in which she did cover in completing this job and returning back to collect her books.
Now, the miximum distance she travelled carrying a flag = Distance travelled by Ruchi during placing the 14th flag in her left position
`=(2+2+2+ ... +13" times")`
`=2xx13=26m`
Hence, the required maximum distance she travelled carrying a flag is 26 m.