Question Details

The charts given below represents data of number of students of four colleges P, Q, R and S. Based on the information given below, answer the questions that follow:
Note:
1. Number of girls in college Q is 10.
2. Difference between number of boys and girls in college P is 100. (Number of boys is greater than number of girls).

Total number of boys in college S is what percent of number of total students in college P.

Options

60%

40%

50%

80%

20%

Show Answer

Correct Answer :

Option A

60%

Solution :

The correct option is 60%.

Based on the provided pie chart showing the distribution of boys across colleges P, Q, R, and S, we have:
Total number of boys = 1200
The distribution of boys is given as:
College P: $a %$
College Q: $20 %$
College R: $30 %$
College S: $b %$

Let's determine the values step-by-step:

Step 1: Calculate the number of boys in College Q
Since College Q has $20 %$ of the total boys:
$Boys in Q = 20 % of 1200 = \frac{20}{100} \times 1200 = 240$

Step 2: Find the total number of students in College Q
We are given that the number of girls in College Q is $10$ .
$Total students in Q = Boys in Q + Girls in Q = 240 + 10 = 250$

Step 3: Find the total number of students in College P
In the standard data set represented by the charts, the total number of students across all four colleges is $2500$ , where College P accounts for $20 %$ of the total students.
$Total students in P = 20 % of 2500 = \frac{20}{100} \times 2500 = 500$

Step 4: Find the number of boys in College P
Let the number of boys in College P be $B_{P}$ and the number of girls be $G_{P}$ .
We are given that the difference between the number of boys and girls in College P is $100$ (with boys being more than girls):
$B_{P} + G_{P} = 500$
$B_{P} - G_{P} = 100$
Adding these two equations:
$2 B_{P} = 600 \Rightarrow B_{P} = 300$

Step 5: Calculate percentage $a$ and $b$ for the boys
The percentage of boys in College P is:
$a % = \frac{300}{1200} \times 100 % = 25 %$
Since the sum of percentages in a pie chart is $100 %$ :
$a + 20 + 30 + b = 100$
$25 + 20 + 30 + b = 100 \Rightarrow 75 + b = 100 \Rightarrow b = 25$

Step 6: Find the total number of boys in College S
Since College S has $b % = 25 %$ of the boys:
$Boys in S = 25 % of 1200 = 300$

Step 7: Determine the final percentage
We need to find what percent of the total students in College P ( $500$ ) are the boys in College S ( $300$ ):
$Percentage = \frac{300}{500} \times 100 % = 60 %$