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

Let's solve the problem step-by-step by analyzing the scatter chart and the given information.

Step 1: Understand the Data from the Scatter Chart

The scatter chart displays the number of boys on the Y-axis and the number of girls on the X-axis for three classes: P, Q, and R.

From the chart, we can extract the following values:

For Class P:
Number of boys (Y-axis) = 40
Number of girls (X-axis) = a + b

For Class Q:
Number of boys (Y-axis) = 20
Number of girls (X-axis) = a + 3b

For Class R:
Number of boys (Y-axis) = 60
Number of girls (X-axis) = a + 5b

Step 2: Find the number of girls in class R

We are given the note: "If there were 10 more girls in class R then the probability of selecting a girl from R would be 40%"

Let the 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 total number of students in class R becomes $G_R+60+10=G_R+70$.

The probability of selecting a girl under this condition is 40% (or $\frac{2}{5}$):

$\frac{G_R+10}{G_R+70}=\frac{2}{5}$

Cross-multiplying to solve for $G_R$:
$5(G_R+10)=2(G_R+70)$
$5G_R+50=2G_R+140$
$3G_R=90$
$G_R=30$

Thus, the number of girls in class R is 30, and the total number of students in class R is:
Total students in R = $60+30=90$.

Step 3: Calculate the number of girls in class R who opt for the science stream

We are given that $11\frac{1}{9}\%$ of students in class R opt for the science stream.

Converting the percentage to a fraction:
$11\frac{1}{9}\%=\frac{100}{9}\%=\frac{1}{9}$

Number of science students in R = $\frac{1}{9}\times 90=10$.

The ratio of boys to girls among these science students is 7:3.

Therefore, the number of girls in class R who opt for the science stream is:
$10\times \frac{3}{7+3}=3$.

Step 4: Find the total number of girls in class Q

We are given that the girls who opt for the science stream in class R (which is 3) is $16\frac{2}{3}\%$ of the total girls in class Q ($G_Q$).

Converting the percentage to a fraction:
$16\frac{2}{3}\%=\frac{50}{3}\%=\frac{1}{6}$

So, we can set up the equation:
$\frac{1}{6}\times G_Q=3$
$G_Q=18$

So, the number of girls in class Q is 18.

Step 5: Find the total number of students in class Q

From the scatter chart, the number of boys in class Q is 20.

Total number of students in class Q = Boys in Q + Girls in Q
Total students in Q = $20+18=38$.