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Variation Problem

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by knight247 » Wed Jun 29, 2011 10:55 am
During a survey of company Y, Jay observes that the duration, d, in which work gets completed in the company is inversely proportional to the sum of two quantities, the efficiency, e, of workers and the number of workers, n; each of these two quantities is directly proportional to x. It is also seen that e = 1, n = 10 and d = 3 whenever x = 2. Which of the following is a correct representation of d in terms of x?

(A) d=3/(0.5x+10)
(B) d=2x/(0.5+5x)
(C) d=x/x-5
(D) d=6/x
(E) d=1/(1+x)

OA is D

Detailed explanations would be appreciated
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by baladon99 » Wed Jun 29, 2011 11:57 am
First step is to find the value of all the constants in the problem

Given d = p /(e+n) where p is a constant
and also e = qx ; n = rx where q & n are constants.

Plug in the given values when x =2 in the 1st eqn

3 = p/(1+10)
p=33

Plug in the values in rest of the eqns
1 =2q ; q =1/2---> e= x/2
10 = 2r ; r=5-----> n= 5x

substitute these vales in 1st eqn by keeping x as it is
d= 33/(x/2+5x)
d=6/x
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by amit2k9 » Thu Jun 30, 2011 3:25 am
e=0.5 x
n= 5x
e+n = 5.5x

d=3= k/5.5x giving k = 5.5*2*3 = 33
thus
d= 33/5.5x = 6/x.D
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