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 responsiblity of palcing 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?

Answer 1

Let A be the middlemost point and 13 flags are fixed at points A₁, A₂ , A₃ ....A₁₃ to the left of A and remaining to the right of A.

Distance travelled for fixing & coming back to A for

(i) first flag = (2+2)m = 4m = a

(ii) second flag = (4+4)m = 8m = a₂

(iii) third flag = (6+6)m = 12m = a₃

∴ a, a₂ , a₃ ... from an AP in which a = 4 , a₂ = 8 , a₃ = 12.... n = 13 and common difference, d = 8 - 4 = 4.

S_n = ( n /2) [ 2a = (n -1) d]

∴ S 13 = (13/2) [2 × 4 + (13 - 1)4]

= (13/2) (8+48)

= (13/2) × 56

= 364

∴ Distance travelled to fix 13 flags to the left of A = 364m

Similarly, distance travelled to fix remaining 13 flags to the right of A = 364m

∴ Total distance travelled = 2 × 364 m
= 728m

Now, the maximum distance she travelled carrying a flag = Distance travelled by Ruchi during placing the 14th flag in her left position or 27th flag in her right position

= (2 + 2 + 2 + ... + 13 times)

= 2 × 13 = 26 m

Hence, the maximum distance she travelled carrying a flag is 26 m.