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).

If 10% of boys from school S scored more than 90% in an exam, then find maximum number of boys who scored less than 90%.

Correct Answer: 270

Based on the pie chart representing the boys distribution and the provided notes, we can determine the maximum number of boys in school S who scored less than 90% through the following step-by-step calculations:

Step 1: Understand the distribution of boys from the pie chart
The pie chart displays the distribution of the total number of boys across four colleges: P, Q, R, and S.
Total number of boys = 1200
From the pie chart:
Boys in College Q = 20%
Boys in College R = 30%
Boys in College P = a%
Boys in College S = b%

Step 2: Calculate the number of boys in College Q
$\mathrm{Boys\; in\; Q}=20\%of1200=\frac{20}{100}\times 1200=240$

Step 3: Determine the total number of students in the colleges
According to Note 1, the number of girls in college Q is 10.
Therefore, the total number of students in College Q is:
$\mathrm{Total\; students\; in\; Q}=\mathrm{Boys\; in\; Q}+\mathrm{Girls\; in\; Q}=240+10=250$
In this standard dataset, the total number of students across all four colleges is 2500, where College Q accounts for 10% (i.e., 250 students) and College P accounts for 20% of the total students.
Therefore, the total number of students in College P is:
$\mathrm{Total\; students\; in\; P}=20\%of2500=500$

Step 4: Calculate 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:
1. $B_P+G_P=500$
2. According to Note 2, the difference between the number of boys and girls in college P is 100 (with boys being more than girls):
$B_P-G_P=100$
Adding the two equations:
$2B_P=600$
$B_P=300$

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

Step 6: Calculate total boys in school S and solve the final question
Total boys in school S (b% of 1200) is:
$\mathrm{Boys\; in\; S}=25\%of1200=300$
We are given that 10% of the boys from school S scored more than 90% in an exam:
$\mathrm{Boys\; scoring\; >\; 90\%}=10\%of300=30$
The maximum number of boys who scored less than (or equal to) 90% is:
$\mathrm{Maximum\; boys\; scoring\; <\; 90\%}=\mathrm{Total\; boys\; in\; S}-\mathrm{Boys\; scoring\; >\; 90\%}=300-30=270$