Everything you need to know about Tree Structures - Exercise Question #1

In a law firm, 72% of the employees are associates and 54% of the employees are senior associates. What percent of the associates in the firm are junior associates?

A. 18%
B. 25%
C. 50%
D. 54%
E. 75%

To solve question 2: Question 2

To read the article: Everything you need to know about Tree Structures


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I believe that it should be A. Because lets assume we have 100 employees in the firm. And 72 (72%) of them are associates and 54(54%) are Senior associates.

Now 72-54=18 are junior associates. which means 18% of 100.

Solution

Given:
We are given that,

• 72% of the employees, in a law firm, are associates, and
• 54% of the employees are senior associates

To find:

• We are asked to find out the percent of the associates, who are junior associates

Approach and Working:

• Total employees must be divided into two categories, they are associates and others.
• Associates are then further divided into senior associates and junior associates

Now, let’s represent the above structure in the form a tree diagram.



Now, let’ see what we need to find: The percentage of associates, in the firm, who are junior associates = \((\frac{A_J}{A}) * 100\)

• Thus, we need to find the values of \(A_J\) and \(A_S\), to answer this question

Let us assume that the total number of employees in the firm = T

• From the given information , we can say that the number of associates, A = 72% of T = \(\frac{72T}{100}\)

Now, from the diagram we can see that, total number of associates, \(A = A_J + A_S\)

• And, we are given that \(A_S\) = 54% of T = \(\frac{54T}{100}\)
• Which implies, \(A_J = A - A_S = \frac{72T}{100} – \frac{54T}{100} = \frac{18T}{100}\)

Thus, \((\frac{A_J}{A}) * 100 = [(\frac{18T}{100})/ (\frac{72T}{100})] * 100 = 18 * \frac{100}{72} = 25%\)

Therefore, the percentage of associates, in the firm, that are junior associates = 25%



Hence, the correct answer is option B.

Answer: B


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