tough rate and proportion prob

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

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.