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The value of a share was 25% less in the 2nd quarter over the 1st Updated on: 12 Aug 2018, 23:35
Originally posted by EgmatQuantExpert on 13 Jun 2018, 04:12.
Last edited by EgmatQuantExpert on 12 Aug 2018, 23:35, edited 2 times in total.
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3 Major Concerns Students Face in Solving Percentage Problems - Exercise Question #2


The value of a share was 25% less in the 2nd quarter over the 1st quarter, and 20% more in the 3rd quarter over the 2nd quarter. What should be the percentage change in the value from 3rd to 4th quarter, if the percentage increase of the value from 1st to 4th quarter is 20%?

    A. -33.3%
    B. -20%
    C. 0
    D. +20%
    E. +33.3%


To solve question 3: Question 3

To read the article: 3 Major Concerns Students Face in Solving Percentage Problems
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The value of a share was 25% less in the 2nd quarter over the 1st 13 Jun 2018, 04:43
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1st quarter ---> x and assume x=100
2nd quarter ---> 0.75*100=75
3rd quarter ---> 75*1.2=90
4th quarter ---> 1.2*100=120

The difference betw 3rd and 4th quarters is 30. the increase from 3rd to 4th will be (30/90)*100

In My opinion
Ans: E
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The value of a share was 25% less in the 2nd quarter over the 1st 13 Jun 2018, 04:52
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EgmatQuantExpert
3 Major Concerns Students Face in Solving Percentage Problems - Exercise Question #2


The value of a share was 25% less in the 2nd quarter over the 1st quarter, and 20% more in the 3rd quarter over the 2nd quarter. What should be the percentage change in the value from 3rd to 4th quarter, if the percentage increase of the value from 1st to 4th quarter is 20%?

    A. -33.3%
    B. -20%
    C. 0
    D. +20%
    E. +33.3%
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Let the share cost be $100 in the first quarter.

Since there is a 25% reduction in the price of the share from the 1st quarter to the
2nd quarter, the cost of the share will be 0.75*100 = $75.

In the 3rd quarter, there is a 20% increase, the cost of the share is 1.2*$75 = $90.

For the share to be 20% costlier in the 4rth qtr when compared to the 3rd quarter,
the share must be 1.2*$100 or $120. There must be a $30 increase in the cost.

Therefore, the percentage increase from the 3rd quarter to the 4th quarter is \(\frac{$30}{$90} * 100\) = +33.3%(Option E)
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The value of a share was 25% less in the 2nd quarter over the 1st 13 Jun 2018, 06:30
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Given:
Q1 - Q2 = -25%
Q2 - Q3 = +20%
Q3 - Q4 = ?
If Q1 - Q4 = +20%

Let the value of share be $100 in Q1.
Then, its value in Q2 = $75 ( Q1 - Q2 = -25% )
Value of share in Q3 = $90 ( Q2 - Q3 = +20% )
Value in Q4 if Q1 - Q4 = +20% will be $120.
So, Q3 - Q4 is $90 - $120.

%change = \(\frac{(120 - 90)}{90} x 100\)

% change = 33.33%

Option E
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The value of a share was 25% less in the 2nd quarter over the 1st 16 Jun 2018, 11:35
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Solution



Given:
The value of a share was
    • 25% less in the 2nd quarter over the 1st quarter
    • 20% more in the 3rd quarter over the 2nd quarter
    • 20% more in the 4th quarter over the 1st quarter

To find:
    • The percentage change in the value from 3rd to 4th quarter

Approach and Working:
Let us assume the value of the share in the 1st quarter is 100
    • The value in the 2nd quarter = \(100 * 0.75 = 100 * \frac{3}{4}\) = 75
    • The value in the 3rd quarter = \(75 * 1.2 = 75 * \frac{6}{5}\) = 90
    • The value in the 4th quarter = \(100 * 1.2 = 100 * \frac{6}{5}\) = 120

As the value in the 4th quarter is more than the value in the 3rd quarter, the percentage change will indicate percentage increase
    • The percent increase from 3rd quarter to 4th quarter = \(\frac{120 – 90}{90} * 100 = \frac{30}{90} * 100 = \frac{1}{3} * 100\) = 33.33%

Hence, the correct answer is option E.

Answer: E

Important Note Related to the Article


    • The question does not mention any specific values, rather it only mentions the change in percentages. Hence, we can assume the value as 100 and do the calculation.
    • The question can also be solved in the same manned, assuming the 1st quarter value to be an unknow variable, say x.
    • Many-a-times the calculation becomes much easier, if the percentage changes are converted into fractions.
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The value of a share was 25% less in the 2nd quarter over the 1st 29 Sep 2022, 05:36
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