Question : 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.
(a) How much distance did she cover in placing 6 flags on either side of centre point? [1 Marks]
(b) Represent above information in Arithmetic progression. [1 Marks]
OR
How much distance did she cover in completing this job and returning to collect her books?
(c) What is the maximum distance she travelled carrying a flag? [2 Marks]
Doubt by Prateek
Solution :
Total Flags = 27
Distance between two flags = 2 m
Position of Ruchi = Middle Flag
Here
n=27 (odd)
Middle Flag = (n+1)th/2
=(27+1)th/2
=28th/2
=14th
Position of Ruchi = Middle Flag
Here
n=27 (odd)
Middle Flag = (n+1)th/2
=(27+1)th/2
=28th/2
=14th
So Ruchi is standing at the position of 14th flag
and there are 13 flags on the both the side of her position.
and there are 13 flags on the both the side of her position.
Distance covered by Ruchi in putting the first flag nearest to her position and then returning back on one side only = 2(2) = 4 m
Distance covered by Ruchi in putting the second flag nearest to her position and then returning back on one side only = 2(2+2)
=2(4)
= 8 m
Distance covered by Ruchi in putting the third flag nearest to her position and then returning back on one side only = 2(2+2+2)
=2(6)
= 12 m
and so on.
So the required AP would be . . .
4, 8, 12 . . .
Distance covered by Ruchi in putting the second flag nearest to her position and then returning back on one side only = 2(2+2)
=2(4)
= 8 m
Distance covered by Ruchi in putting the third flag nearest to her position and then returning back on one side only = 2(2+2+2)
=2(6)
= 12 m
and so on.
So the required AP would be . . .
4, 8, 12 . . .
Here
a=4
d=a2-a1
d=8-4
d=4
a=4
d=a2-a1
d=8-4
d=4
(a) n=6
Sn=n/2[2a+(n-1)d
S13=6/2[2(4)+(6-1)4]
S13=3[8+(5)4]
S13=3[8+20]
S13=3[28]
S13=3[28]
S13=84
S13=6/2[2(4)+(6-1)4]
S13=3[8+(5)4]
S13=3[8+20]
S13=3[28]
S13=3[28]
S13=84
The distance covered by Ruchi in placing 6 flags on either side of centre point is 84 m
(b) The required AP would be 4, 8, 12 . . .
OR
Distance covered in putting all 13 flags on one side
Sn=n/2[2a+(n-1)d
S13=13/2[2(4)+(13-1)4]
S13=13/2[8+(12)4]
S13=13/2[8+48]
S13=13/2[56]
S13=13[28]
S13=364
Total distance covered by Ruchi in putting the flags on both the sides = 2×364
= 728 m
Distance covered in putting all 13 flags on one side
Sn=n/2[2a+(n-1)d
S13=13/2[2(4)+(13-1)4]
S13=13/2[8+(12)4]
S13=13/2[8+48]
S13=13/2[56]
S13=13[28]
S13=364
Total distance covered by Ruchi in putting the flags on both the sides = 2×364
= 728 m
(c) Maximum distance Ruchi covered while carrying the flag will be the distance covered in putting the last flag = 2[13]
=26 m