The scatter chart below shows the number of boys (Y-axis) and number of girls (X-axis) in three different classes: P, Q, and R.

Note: If there were 10 more girls in class R, then the probability of selecting a girl from class R would be 40%.
![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759774420/aptidude_questions/kqpjkabrj8deisxeuyaq.png)
If the number of girls in class P is 25\% of the number of boys in class P, find the difference between the total number of students in class P and class Q.

Question

The scatter chart below shows the number of boys (Y-axis) and number of girls (X-axis) in three different classes: P, Q, and R.

Note: If there were 10 more girls in class R, then the probability of selecting a girl from class R would be 40%.
![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759774420/aptidude_questions/kqpjkabrj8deisxeuyaq.png)
If the number of girls in class P is 25\% of the number of boys in class P, find the difference between the total number of students in class P and class Q.

Accepted Answer

**Solution:**

1. Let the number of boys and girls in class R be $ B_R $ and $ G_R $ respectively.

2. Given that if there were 10 more girls in class R, the probability of selecting a girl from class R would be 40\%. This means:
   $$
  $ \frac{G_R + 10}{B_R + G_R + 10} = 0.4 $
   $$

3. Rearranging:
   $$
   $G_R + 10 = 0.4 (B_R + G_R + 10)$
   $$
   $$
   $G_R + 10 = 0.4 B_R + 0.4 G_R + 4$
   $$
   $$
   $G_R - 0.4 G_R = 0.4 B_R + 4 - 10$
   $$
   $$
  $ 0.6 G_R = 0.4 B_R - 6$
   $$
   $$
   $3 G_R = 2 B_R - 30$
   $$

4. From the scatter plot (approximate values):
   - Class P: Boys $ $B_P = 40$ $, Girls $ $G_P = 10$ $ (since girls are 25\% of boys, $ $0.25 \times 40 = 10 $$)
   - Class Q: Boys $ $B_Q = 20$ $, Girls $ $G_Q = 20$ $ (from the scatter plot)

5. Calculate total students in class P:
   $$
  $ T_P = B_P + G_P = 40 + 10 = 50$
   $$

6. Calculate total students in class Q:
   $$
   $T_Q = B_Q + G_Q = 20 + 20 = 40$
   $$

7. Find the difference:
   $$
   $T_P - T_Q = 50 - 40 = 10$
   $$

**Answer:** 10

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