Problem Solving

An engine moves at the speed of 48 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 4 coaches are attached speed decreases to 36 kmph.What will be the speed of train when 36 coaches are attached.

A ) 24
B ) 36
C ) 12
D ) 0
E ) 18

The OA is C.

Is there a strategic approach to this question? Can any experts help me, please? Thanks!

AAPL wrote:An engine moves at the speed of 48 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 4 coaches are attached speed decreases to 36 kmph.What will be the speed of train when 36 coaches are attached.

A ) 24
B ) 36
C ) 12
D ) 0
E ) 18

The OA is C.

Is there a strategic approach to this question? Can any experts help me, please? Thanks!

Call the number of coaches 'c'. If the reduction in speed is proportional to the square root of the number of coaches, we know the reduction is proportional to √ c, meaning we'll find the reduction by multiplying √ c by some constant. We'll call that constant 'k.'

Now we have: Reduction = k * √ c

We're told that when c = 4, the reduction is 12 (because the speed decreases from 48-36.) Now we have 12 = k * √ 4 --> 12 = k *2 ----> 6 = k

We want the reduction amount when we have 36 coaches. If c = 36, and we calculated that k = 6, then Reduction = 6 * √ 36 = 6*6 = 36.

If the initial speed is 48, and that speed is reduced by 36, the new speed will be 48 - 36 = 12. The answer is C