Proportions

[moneyman]

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversly proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

100% decrease
50% dec
40% dec
40% inc
50% inc

OA is D

Guys pls explain the logic behind this question..This is from GMAT Test Prep

[camitava]

Moneymen,
let r = rate
a = con of solution a
b = con of sol b

now by Qs, r prop a^2 and r prop 1/b
so r = ka^2/b where k = constant
now con of b has increased by 100% so new con of b is = 2b
so new rate, r1 = ka1^2/2b but r1 = r
so ka1^2/2b = ka^2/b so a1 = sqrt(2) * a = 1.414a
so % increase = (1.414a - a) * 100 / a = 41%
so imo d.
Moneyman, here I have a request - if u r feeling not comfortable with proportionality, then suggest u to do some Google search on proportion.

[moneyman]

Hi Amitava,
I am ok with proportions but here I cuold not construct the question well.Also can u pls tell me why have u used the constant k in your answer?? I mean what importanc does it have??

[camitava]

Maxx,
suppose, u r having a proportion a prop b. That means a = kb where k is some constant. now with some real life example -
say a prop b. and when a = 2, b = 10; a = 3, b = 15; a = 4, b = 20. so here k, the constant term is = 10/2 = 15/3 = 20/4 = 5. Got it now? and this is a basic principle in proportion when a prop b and a prop 1/c then a prop b/c.