Question

Question 10
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 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

Given that, 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.
Given that, the number of flags = 27 and distance between each flag = 2 m.
Also, the flags are stored at the position of the middle most flag, i.e., ${14}^{th}$ flag and Ruchi was given the responsibility of placing the flags. Ruchi kept her books, where the flags were stored i.e., ${14}^{th}$ flag and she could carry only one flag at a time.
She placed 13 flags into her left position from middle most flag i.e., ${14}^{th}$ flag. For placing second flag and return his initial position distance travelled = 2 + 2 = 4m.
Similarly, for placing third flag return his initial position, distance travelled = 4 + 4 = 8 m
For placing forth flag and return his initial position, distance travelled = 6 + 6 = 12 m.
For placing the fourteenth flag and return his initial position, distance travelled
= 26 + 26 = 52 m
Proceeding in the same manner into her right position from middle most flag i.e., ${14}^{th}$ flag.
Toal distance travelled, in that case, = 52m
Also, when Ruchi placed the last flag she returns his middle most position and collects her books. This distance also included in placing the last flag.
So, these distances form a series.
4 + 8 + 12 + 16 + . . . . .+52 [for left]
and 4 + 8 + 12 + 16 + . . . . .+ 52 [for right]
$\therefore$ Total distance covered by Ruchi for placing these flags,
= 2 $\times$ (4 + 8 + 12 + . . . . .+ 52)
$=2\times \left[\frac{13}{2}\right\{2\times 4+(13-1)\times (8-4)\left\}\right]\left\{\frac{\because SumofntermsofanAP}{S_n=\frac{n}{2}[2a+(n-1\left)d\right]}\right\}$
$=2\times \left[\frac{13}{2}\right(8+12\times 4\left)\right]$
[$\because$ both sides of Ruchi number of flags ie., n = 13]
$=2\times \left[13\right(4+12\times 2\left)\right]=2\times 13(4+24)$
$=2\times 13\times 28=728m$
Hence, the required is 728 m in which she did cover in completing this job and returning back to collect her books.
Now, the maximum distance she travelled carrying a flag = Distance travelled by Ruchi during placing the ${14}^{th}$ flag in her left position or ${27}^{th}$ flag in her right position.
= (2 + 2 + 2 + . . . . .+ 13 times)
= 2 $\times$ 13 = 26 m
Hence, the required maximum distance she travelled carrying a flag is 26 m.