The students of a shool decided to beautifly 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 wer 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

Total number of flags = 27
`:.` Middle most flag `=(27+1)/(1)`th i.e., 14th

When Ruchi moves from 14th flag to 13th flag and comes back then it is 1st round and she has to travel (2+2)i.e., 4m, i.e., `2[(14-13)xx2]` .
Now, she goes from 14th to 12th and comes back, then it is 2nd round and she has to travel (4|4) i.e. 8m i.e. `2[(14-12)xx2]`.
Similarly, in 13th round, she has to travel `2[(14-1)xx2]` i.e. 52 cm.
So, total distance of one side (left side) `=4+8+...+52` which is an A.P.
Similarla, total distance of right side =4+8+...+52
So, total distance Ruchi has to cover `=2xx(4+8+...+52)`
`=2xx4(1+2+...+13)`
`=8xx(13)/(2)(1+13) " " ` [`:' S_(n)=(n)/(2)(a+l)`]
`=52xx14=728m`.
Now, the maximum distance she travelled carrying one flag only
=distance covered from 14th flag to 1st flag
`=(14-1)xx2=26m`