Question Details

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%

If the number of girls in class P is 25% of the number of boys in the class P, then find the difference between the total students in class P and Q.

Options

Show Answer

Correct Answer :

Option D

Solution :

Correct Answer: 10

Based on the provided scatter chart, the Y-axis represents the number of boys in each class, and the X-axis represents the number of girls in each class. From the plot, we can extract the following data for each class:
1. Class P:
Number of boys ( $B_{P}$ ) = 40
Number of girls ( $G_{P}$ ) = $a + b$
2. Class Q:
Number of boys ( $B_{Q}$ ) = 20
Number of girls ( $G_{Q}$ ) = $a + 3 b$
3. Class R:
Number of boys ( $B_{R}$ ) = 60
Number of girls ( $G_{R}$ ) = $a + 5 b$

Step 1: Use the information for Class R to find the value of $a + 5 b$
We are given that if there were 10 more girls in class R, the probability of selecting a girl from class R would be 40% (or $\frac{2}{5}$ ).
Let the new number of girls be $G_{R} + 10$ .
The new total number of students in class R would be:
$Total students = B_{R} + G_{R} + 10 = 60 + G_{R} + 10 = G_{R} + 70$

Setting up the probability equation:
$\frac{G_{R} + 10}{G_{R} + 70} = \frac{2}{5}$
Cross-multiplying to solve for $G_{R}$ :
$5 (G_{R} + 10) = 2 (G_{R} + 70)$
$5 G_{R} + 50 = 2 G_{R} + 140$
$3 G_{R} = 90$
$G_{R} = 30$
Thus, we have:
$a + 5 b = 30$ --- (Equation 1)

Step 2: Use the information for Class P to find the values of $a$ and $b$
The number of girls in class P ( $G_{P}$ ) is 25% of the number of boys in class P ( $B_{P}$ ):
$G_{P} = 0.25 \times 40 = 10$
Thus, we have:
$a + b = 10$ --- (Equation 2)

Now, subtract Equation 2 from Equation 1:
$(a + 5 b) - (a + b) = 30 - 10$
$4 b = 20$
$b = 5$
Substituting $b = 5$ back into Equation 2:
$a + 5 = 10 \Rightarrow a = 5$

Step 3: Calculate the total number of students in Class P and Class Q
For Class P:
Total students in P = $B_{P} + G_{P} = 40 + 10 = 50$

For Class Q:
Number of girls in Q ( $G_{Q}$ ) = $a + 3 b = 5 + 3 (5) = 20$
Total students in Q = $B_{Q} + G_{Q} = 20 + 20 = 40$