Latest CAT Aptitude Question SOLUTION: After striking the floor, a ball rebounces 45th of its height from which it has fallen. If it is dropped from a height of 120m, the total distance it travels before coming to rest

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After striking the floor, a ball rebounces 45th of its height from which it has fallen. If it is dropped from a height of 120m, the total distance it travels before coming to rest is

Asked In CAT chaitanya (11 years ago)

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vishnu  (11 years ago)

There's a theorem that states:
The infinite sum = a/(1-r)
a = the starting number, in this case 120.
r = the change ration, again, in this case 1/45.
But, this only accounts for half of the travel, we need to take in account the bounce back. So, we multiply it by 2.
So, we have:
2a/(1-r) = 2(120)/(1-1/45) = 245.45
But, since the intial drop (120) isn't met twice, we need to subtract this from our answer above.
So,
245.45m - 120 = 124.95m

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phani  (11 years ago)

The infinite sum in GP = a/(1-r)
a = the starting number
r = the common ratio in this case 1/45

IT FALLSS FROM 120M.
AFTER THAT 2(120/45+120/ 45^2+120^45^3+.........)
=120*2(1/45+1/45^2+........)
=240(1/45/(1-1/45))(sun of Infinite terms)
=5.455

TOTALLY IT TRAVELS 120+5.455=125.455M

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vishnu  (11 years ago)

sorry in the first solution posted by me there is sligtly mistake in subtraction. this is correct solution after modification of that.



There's a theorem that states:
The infinite sum = a/(1-r)
a = the starting number, in this case 120.
r = the change ration, again, in this case 1/45.
But, this only accounts for half of the travel, we need to take in account the bounce back. So, we multiply it by 2.
So, we have:
2a/(1-r) = 2(120)/(1-1/45) = 245.45
But, since the intial drop (120) isn't met twice, we need to subtract this from our answer above.
So,
245.45m - 120 = 125.45m

Is this solution Helpfull? Yes | No   

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