The students of a school decided to beautify the school on an annual day by fixing colorful 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 in 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 traveled carrying a flag?

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830 m, 20 m

728 m, 26 m

619 m, 53 m

513 m, 19 m

answer is B.

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Detailed Solution

Let the flags be numbered from 1 to 27.
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Distance between every two consecutive flags is 2 m.
Now, rename the 14th flag as the 0th flag and the 13 flags either side from 1 to 13.
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As the total number of flags is 27, there would be 13 flags on one side, 13 flags on the other side and one flag in the middle.
Consider that she fixes 13 flags on one side of the middle flag.
So, the distance covered by Ruchi to fix the first flag and return is:

The distance covered by Ruchi to fix the second flag and return is:

Similarly, the distance covered by Ruchi to fix the thirteenth flag and return is:

The total distance traveled by Ruchi to fix the flags and return back is:

Therefore, the total distance covered by Ruchi only to carry the flag is:

And the maximum distance traveled by Ruchi carrying a flag is to put the 13th flag on the right side and left side. Therefore, the maximum distance traveled carrying a flag is:

Hence, the option 2 is correct- 728 m, 26 m.

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