SECTION – 1

 

16.  The Howrah-Puri express can move at 45 km/hour without its rake, and the speed is diminished by a constant that varies as the square root of the number of wagons attached. If it is known that with 9 wagons, the speed is 30 km/hour, what is the greatest number of wagons with which the train can just move?

A.    63                                               B.    64                                               C.   80                                               D.   81

 

Solution:

 

Without any wagons, the speed is 45 km/hr. The speed diminishes by a quantity that varies (directly) as the square root of the number of wagons attached (∵ By default, variation is direct).

Let the quantity (by which the speed diminishes) be Q, the number of wagons attached be N.

        = a constant = K (say). Þ Q = k

 

       When Q = 45 – 30 = 15, N = 9. ∴ K =  =  5

 

       When the train can just move, its speed

       = 45 – 5 would be slightly more than 0.

 

∴ 45 would be slightly more than 5

 

∴ would be slightly less than  = 9.

 

∴ N would be slightly less than 92 = 81

∴ The greatest value of N is 80                                                                                                                                                                     Choice (C)