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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

Solution:

Given, the students decided to fix colourful flags on the straight passage of the school.

Also, there are 27 flags which are to be fixed at intervals of every 2 m.

We have to find the maximum distance she travelled carrying a flag.

The flags are stored at the position of the middle most flag.

Ruchi kept her books where the flags were stored.

Ruchi could carry only one flag at a time.

Here, number of flags, n = 27

The middle flag post is at (n + 1)/2 = (27 + 1)/2 = 28/2 = 14th post

Let us consider that Ruchi first fixes 13 flags on the left side and then completes fixing 13 flags on the right side.

From the middle post she carries one flag to 2m, fixes it and then returns 2m to the middle post.

So, she travels 2 + 2 = 4 m

Similarly, to fix the second flag she travels 4 + 4 = 8 m

To fix the third flag she travels 8 + 4 = 12 m

So, this forms a series

The series is 4, 8, 12, 16,......

Here, first term, a = 4

Common difference, d = 4

Number of flags, n = 13

The sum of the first n terms of an AP is given by

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

So, S = 13/2[2(4) + (13 - 1)(4)]

= 13/2[8 + 12(4)]

= 13/2[8 + 48]

= 13/2[56]

= 13(28)

= 364 m

So, she travels 364 m to fix flags on the left of the middle post.

So, total distance travelled by her to fix all the flags = 2(364) = 728 m.

Now, the distance travelled by Ruchi carrying the flag

= 728/2

= 364 m

Therefore, the maximum distance travelled by Ruchi carrying the flag is 364 m.

✦ Try This: 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 49 flags to be fixed at intervals of every 3 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

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.4 Problem 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

Summary:

If 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. The distance Ruchi covered in completing this job and returning back to collect her books is 728 m. The maximum distance she travelled carrying a flag is 364 m.

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