Directions (48-51): The scatter chart given below shows the number of boys on (Y – axis) and number of girls (X – axis) in three different class of P, Q and R.

NOTE: If there were 10 more girls in class R then the probability of selecting a girl from R would be 40%

The scatter chart given below shows the number of boys on (Y – axis) and number of girls (X – axis) in three different class of P, Q and R.

NOTE: If there were 10 more girls in class R then the probability of selecting a girl from R would be 40%

If $11\frac{1}{9}\%$ of students in class R opt science stream and the ratio of boys and girls is 7:3 and the girls who opt science stream in class R is $16\frac{2}{3}\%$ of total girls in Q, then find the total number of student in class Q.

Correct Answer: 38

Step-by-step Explanation:

1. Analyze the Scatter Chart:
From the given scatter chart, the Y-axis represents the number of boys and the X-axis represents the number of girls for three different classes: P, Q, and R.
Reading the data points from the chart:
• For class P: Number of boys = 40, and Number of girls = $a+b$
• For class Q: Number of boys = 20, and Number of girls = $a+3b$
• For class R: Number of boys = 60, and Number of girls = $a+5b$

2. Determine the Number of Girls in Class R:
The note states: "If there were 10 more girls in class R then the probability of selecting a girl from R would be 40%."
Let the initial number of girls in class R be $G_R=a+5b$.
The number of boys in class R is $B_R=60$.
If there are 10 more girls, the new number of girls is $G_R+10$, and the new total number of students in R is:

$\text{Total Students}=G_R+10+60=G_R+70$

The probability of selecting a girl becomes 40%, which is equal to $\frac{2}{5}$:

$\frac{G_R+10}{G_R+70}$

Cross-multiplying to solve for $G_R$:

$5(G_R+10)=2(G_R+70)$

$5G_R+50=2G_R+140$

$3G_R=90$

$G_R=30$

Therefore, the number of girls in class R is:

$a+5b=30$ --- (Equation 1)

3. Analyze Students Opting for Science Stream in Class R:
The total number of students in class R is:

$\text{Total Students in R}=\text{Boys}+\text{Girls}=60+30=90$

The percentage of students opting for the science stream in class R is $11\frac{1}{9}\%$, which is equal to the fraction $\frac{1}{9}$.
So, the total number of science stream students in R is:

$90\times \frac{1}{9}=10$

The ratio of boys and girls among the science stream students in class R is given as 7:3.
Since the total number of science students is 10, the number of girls opting for science stream in R is:

$10\times \frac{3}{7+3}=3$

4. Find the Number of Girls in Class Q:
The girls opting for the science stream in class R (which is 3) is equal to $16\frac{2}{3}\%$ of the total girls in Q.
We know that $16\frac{2}{3}\%=\frac{1}{6}$.
Let $G_Q$ be the total number of girls in class Q:

$3=\frac{1}{6}\times G_Q$

$G_Q=18$

Therefore, the number of girls in class Q is:

$a+3b=18$ --- (Equation 2)

5. Calculate the Total Students in Class Q:
The total number of students in class Q is the sum of boys and girls in class Q.
From the chart, the number of boys in class Q is 20.
From our calculations, the number of girls in class Q is 18.
Total students in Q:

$\text{Total Students in Q}=20+18=38$