Question

the students of a school decided to beautify the school on 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 metre the flags are stored the position of the middle most flag Ruchi was given the responsibility of placing the flags Ruchi kept her books were the flags was 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 their books what is the maximum distance travelled carrying a flag

Answer 1


Let A be the middle- most 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.

Sn = ( 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

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

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

Answer 2

Answer:

Here is the ans in the attachment

Explanation :

◆ It is given that there are 27 flags all are kept at the place where the middle flag is posted (O)

And ruchi kept her book there

◆ So, we have to find the total distance travelled by ruchi to post all the flags from (O) which are 2m apart from each other.

◆So, we found the middle flag where ruchi kept her book(O) as 14.

◆ So, there are 13 flags on both the sides of (O).

◆ Let's find the distance travelled by ruchi on one side of middle flag suppose from 'O' to 'A'

◆ As, she have to travel again after posting one flag to position 'O'

So, we found as a1 = 4, a2= 8 ,a3= 12.........

Therefore they are in A.P since we got the difference d = 4.

◆ Now , we found the distance coved by ruchi for posting 13 flags from 'O' to 'A' as 364m.

◆ So, she also travelled 364 m on other side of the middle flag (OB).

◆ There fore, the total distance travelled by ruchi for posting 27 flags is 2×364 = 728 m.

ANS = 728 m.