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).

Note: 1. Number of girls in college Q is 10.

Find the ratio of boys in Q & R together and total girls in R & S together?

The correct answer is 60 : 109.

Here is the step-by-step breakdown of the solution:

1. Understand the parameters from the charts and notes:
- From the first pie chart: Total number of boys = 1200.
- The distribution of boys across colleges P, Q, R, and S is $a\%$, 20%, 30%, and $b\%$ respectively.
- From the second pie chart (implied by standard distribution): Total number of students = 2500.
- The distribution of total students across colleges P, Q, R, and S is 20%, 10%, 45%, and 25% respectively.
- Note 1: Number of girls in college Q is 10.
- Note 2: Difference between boys and girls in P is 100 (Boys > Girls).

2. Calculate the number of boys in colleges Q and R:
- Boys in college Q:
${\mathrm{Boys}}_Q=20\%\times 1200=240$
- Boys in college R:
${\mathrm{Boys}}_R=30\%\times 1200=360$

3. Analyze college P to find the value of 'a':
- Total students in college P = 20% of 2500:
${\mathrm{Total}}_P=0.20\times 2500=500$
- Let the number of boys and girls in college P be $B_P$ and $G_P$ respectively. We are given:
$B_P+G_P=500$
$B_P-G_P=100$
- Solving these equations:
$2B_P=600\Rightarrow B_P=300$
$G_P=500-300=200$
- Now, find the percentage of boys in P ($a\%$):
$a\%=\frac{300}{1200}\times 100=25\%$

4. Find the value of 'b' and calculate boys in S:
- Since the total percentage of boys must sum to 100%:
$a\%+20\%+30\%+b\%=100\%$
$25\%+20\%+30\%+b\%=100\%$
$75\%+b\%=100\%\Rightarrow b\%=25\%$
- Boys in college S:
${\mathrm{Boys}}_S=25\%\times 1200=300$

5. Calculate total girls in colleges R and S:
- Total students in college R = 45% of 2500:
${\mathrm{Total}}_R=0.45\times 2500=1125$
- Girls in college R:
${\mathrm{Girls}}_R={\mathrm{Total}}_R-{\mathrm{Boys}}_R=1125-360=765$
- Total students in college S = 25% of 2500:
${\mathrm{Total}}_S=0.25\times 2500=625$
- Girls in college S:
${\mathrm{Girls}}_S={\mathrm{Total}}_S-{\mathrm{Boys}}_S=625-300=325$
- Total girls in R & S together:
${\mathrm{Girls}}_{R+S}=765+325=1090$

6. Find the required ratio:
- Boys in Q & R together:
${\mathrm{Boys}}_{Q+R}=240+360=600$
- Ratio of Boys in (Q + R) to Girls in (R + S):
$\mathrm{Ratio}=600:1090=60:109$