Along a road lie an odd number of stones placed at intervals of 10m. these stones have to be assembled around the middle stone. a person can carry only one stone at a time. a man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. then the number of stones is
Answers
33 Stones
Step-by-step explanation:
Stones placed at intervals of 10 metres.
A person can carry one stone at a time ,
he covered a distance of 4.8 Km = 4800 m
Let say There are 2n + 1 stones in total ( as odd number of stones)
so there will be n stones each side of middle stone
Man started job from Middle
so distance covered for 1st stone = n * 10 + n * 10 m (as he has to go back to pick the stone And come back with stone
Distance covered for 2nd Stone = (n-1)*10 + (n-1)* 10
So covering all the stones of one side
= 2 * n* 10 + 2(n-1)*10 + 2(n-2)*10 +.................. + 2*3*10 + 2*2*10 + 2*1*10
Middle stone is already there
so for remaining n stones on other he has to do same thing
so distance covered for other sides
= 2n*10 + 2(n-1)*10 + 2(n-2)*10 +.................. + 2*3*10 + 2*2*10 + 2*1*10
Hence total Distance covered =
4n*10 + 4(n-1)*10 + 4(n-2)*10 +.................. + 4*3*10 + 4*2*10 + 4*1*10
= 40 * (n + n-1 + n-2 + ......+3 +2 + 1)
= 40 n (n+1)/2
= 20n (n+1)
Distance covered = 4.8km = 4800m
20n (n+1) = 4800
=> n² + n = 240
=> n² + n - 240 = 0
=> n² - 16n + 15n - 240 = 0
=> n(n - 16) + 15(n - 16) = 0
=> (n + 15)(n - 16) = 0
=> n = 16 ( n = - 15 not possible as number of stones can not be negative)
Number of stones = 2n + 1
=2 * 16 + 1 = 33
33 Stones
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