In a developing country, the price of a stock is directly proportional to the reciprocal of the inflation in the country

[Vincen]

In a developing country, the price of a stock is directly proportional to the reciprocal of the inflation in the country, which is in turn directly proportional to the local diesel prices. The price of the stock is 100 currency units when the inflation is 10 units and when the inflation is 12 units, the local price of the diesel is 60 currency units. By how many currency units should the local diesel price fall so that the price of the stock, which is currently at 200 currency units, increases by 25 percent?

A. 5

B. 10

C. 25

D. 30

E. 40

[spoiler]OA=A[/spoiler]

Source: e-GMAT

[deloitte247]

Let stock price = s
Let inflation = i
Let diesel price = d
$$Given\ that\ s=\frac{k}{i}.......eqn\ 1\ \ \ \ \ \ \ where\ k=cons\tan t$$
$$and\ i\ =l\cdot d..........eqn\ 2\ \ \ \ where\ l=cons\tan t$$
$$for\ eqn\ 1\ when\ i=10,\ s=100$$
$$100=\frac{k}{10}and\ k=100\cdot10=1000$$
$$for\ eqn\ 2\ when\ i=12,\ d=60$$
$$12=l\cdot60\ and\ l=\frac{12}{60}=\frac{1}{5}$$
Substituting the value of i in eqn 2 with the value of i in eqn 1
$$s=\frac{k}{i}where\ i=l\cdot d$$
$$s=\frac{k}{l\cdot d}..........eqn\ 3$$
$$currently\ s=200;\ then\ d\ =??$$
$$u\sin g\ eqn\ 3$$
$$200=\frac{1000}{\frac{1}{5}d}=>\ \frac{200}{5}d=1000$$
$$d=1000\cdot\frac{5}{200}=25$$
With 25% increase to the value of s then s becomes
$$s=200+25\%\ of\ 200\ =>\ s=200+50=250$$
$$and\ d=??\ \ \ \ \ u\sin g\ eqn\ 3;$$
$$250=\frac{1000}{\frac{1}{5}d}=>\frac{200}{5}d=1000$$
$$d=1000\cdot\frac{5}{250}=20$$
The change or fall in diesel price from a stock price 200 to 250 => 25 - 20 = 5

Answer = A