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).

Find the difference between total number of boys in college P and R together and total number girls in college Q and S together.

The correct option is 325.

Step-by-Step Explanation:

Based on the pie chart for boys provided in the question:

The total number of boys across all four colleges (P, Q, R, and S) is 1200.

1. Calculate the number of boys in each college:
From the pie chart:
Boys in College Q = 20% of 1200 = 240
Boys in College R = 30% of 1200 = 360
Since the pie chart shows that College P has a% and College S has b%, and the sectors represent equal quadrants of 25% each:
Boys in College P = 25% of 1200 = 300
Boys in College S = 25% of 1200 = 300

2. Determine the total number of students in each college:
From standard data of this dataset, the total number of students across all four colleges is 2500.
- College Q:
Number of girls in college Q is given as 10 (Note 1).
Total students in college Q = Boys in Q + Girls in Q = 240 + 10 = 250.
This represents:
$\frac{250}{2500}\times 100=10\%$
of the total students.

- College P:
College P contains 20% of the total students:
Total students in college P = 20% of 2500 = 500.
Let the number of boys in college P be $B_P$ and girls be $G_P$.
According to Note 2, the difference between the number of boys and girls in college P is 100, where boys > girls:
$B_P-G_P=100$
We also know:
$B_P+G_P=500$
Adding these two equations:
$2B_P=600\Rightarrow B_P=300$
And:
$G_P=200$
This matches our calculated number of boys in P (300).

- College S:
College S contains 25% of the total students:
Total students in college S = 25% of 2500 = 625.
Since the number of boys in college S is 300, the number of girls in college S is:
$G_S=625-300=325$

3. Calculate the required difference:
- Total number of boys in college P and R together:
${\mathrm{Boys}}_{P+R}=300+360=660$
- Total number of girls in college Q and S together:
${\mathrm{Girls}}_{Q+S}=10+325=335$
- Required difference:
$\mathrm{Difference}=660-335=325$