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tough rate and proportion prob

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by quantskillsgmat » Tue Dec 27, 2011 9:51 pm
The reduction in speed of a railway engine is directly proportional to square root of number of compartment attached to it. with no compartments attached speed is 42m/hr. with 9 compartments speed is 24m/hr.what are maximum number of compartments that can be attached to the engine.
a)49
b)48
c)46
d)47
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by user123321 » Wed Dec 28, 2011 4:54 am
quantskillsgmat wrote:The reduction in speed of a railway engine is directly proportional to square root of number of compartment attached to it. with no compartments attached speed is 42m/hr. with 9 compartments speed is 24m/hr.what are maximum number of compartments that can be attached to the engine.
a)49
b)48
c)46
d)47
let Vc is max speed the train can go & V is variable speed it goes.
give reduction in speed is proportional to sqrt(no of compartments). say n is number of compartments.
Vc - V = k(sqrt(n))

given when n=0, then V = 42
=> Vc - 42 = 0
=> Vc = 42
so eq is 42 - V = k(sqrt(n))

given when n=9, then V = 24
=> 42 - 24 = k(sqrt(9))
=> k = 6
so eq is 42 - V = 6(sqrt(n))

so maximum no of compartments that can be accomodated is when V = 0
=> 42 = 6(sqrt(n))
=> n = 49

but if we have Velocity V = 0 then the train will not move, so we need to have 48 i.e 1 less than maximum to have train moved.

[spoiler]IMO 48?[/spoiler]

user123321
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Want to do it right the first time.
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by kanwar86 » Wed Dec 28, 2011 5:20 am
quantskillsgmat wrote:The reduction in speed of a railway engine is directly proportional to square root of number of compartment attached to it. with no compartments attached speed is 42m/hr. with 9 compartments speed is 24m/hr.what are maximum number of compartments that can be attached to the engine.
a)49
b)48
c)46
d)47
IMO, B is the correct answer.
Regards

Kanwar

"In case my post helped, do care to thank. Happy learning :)"
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