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Senior RC Moderator V
Joined: 02 Nov 2016
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Over a period of 2 years from 2010 to 2012, Stock A and Stock B have  [#permalink]

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Question # 41, Date : 10-Nov-2019
This post is a part of Project IR Butler 2019-20. Click here for Details

Over a period of 2 years from 2010 to 2012, Stock A and Stock B have changed in value. In 2010, a share of Stock A and a share of Stock B were, together, worth a total of N dollars. Also, in 2010, the ratio of the price of Stock A to Stock B was 0.8. A and B represent the percent change in value of stocks A and B, respectively from 2012 to 2012. The percent change in a quantity X is calculated using the formula:

$$100∗\frac{X_{new}−X_{old}}{X_{old}}$$

In the table, select the expression that represents the value of Stock B in 2010 and the expression that represents the ratio of Stock A to Stock B in 2012. Make only two selections, one in each column.

 Value of Stock B in 2010 Ratio in 2012 Values N/0.8 N/1.2 N/1.8 A/0.8+B/1.25N 0.8((1+A)/(1+B)) 1.25((1+A)/(1+B))

Spoiler: :: OA
 Value of Stock B in 2010 Ratio in 2012 Values N/0.8 N/1.2 ✔ N/1.8 A/0.8+B/1.25N ✔ 0.8((1+A)/(1+B)) 1.25((1+A)/(1+B))

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Senior RC Moderator V
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Re: Over a period of 2 years from 2010 to 2012, Stock A and Stock B have  [#permalink]

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+1 Kudos to posts containing answer with explanation
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Re: Over a period of 2 years from 2010 to 2012, Stock A and Stock B have  [#permalink]

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For the first column:
Let the value of stock A and the value of stock B be SA and SB.
We know that $$SA+SB= N$$and that $$SA/SB=0.8$$. Therefore $$SB+0.8SB=N$$-> $$SB=N/1.8$$

For the second column, we are asked SA/SB in year 2012. Since the increase in percentage is A and B, SA in 2012 will be equal to $$SA*(1+A)$$and SB will be $$SB*(1+B)$$.
Then, $$SA/SB (in 2012) = \frac{SA*(1+A)}{SB*(1+B)}$$. Since we know that SA/SB is 0.8, the answer is $$\frac{0.8*(1+A)}{(1+B)}$$ Re: Over a period of 2 years from 2010 to 2012, Stock A and Stock B have   [#permalink] 05 Jan 2020, 08:30
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# Over a period of 2 years from 2010 to 2012, Stock A and Stock B have

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