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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

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

by Vincen » Fri Jun 19, 2020 2:52 am

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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

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Source: Beat The GMAT — Problem Solving | Fri Jun 19, 2020 2:52 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

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

by deloitte247 » Sun Jun 21, 2020 12:56 pm

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