Read the information and answer the following questions. There are three classes A, B and C consisting girls and boys. Two teams P and Q are formed. Team P consist of students who plays hockey and team Q who plays football. Each student participated only in one game. The boys in A are x more than the girls. Total girls in B are x and boys are 20 than that of girls. The boys and girls in C are 20% more than that of boys and girls in B respectively. Boys in P is 13 less than that of girls, which is 60% of the combination of girls in two classes (except A and C). Ratio of girls in team P to team Q is 3:4. Boys in P is 50% of the combination of boys of two classes (except A and B).

If 30% of girls from team P joined team Q, and 10% of girls from team Q joined team P, what percentage are the girls in team Q of the girls in team P?

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Question

Read the information and answer the following questions. There are three classes A, B and C consisting girls and boys. Two teams P and Q are formed. Team P consist of students who plays hockey and team Q who plays football. Each student participated only in one game. The boys in A are x more than the girls. Total girls in B are x and boys are 20 than that of girls. The boys and girls in C are 20% more than that of boys and girls in B respectively. Boys in P is 13 less than that of girls, which is 60% of the combination of girls in two classes (except A and C). Ratio of girls in team P to team Q is 3:4. Boys in P is 50% of the combination of boys of two classes (except A and B).

If 30% of girls from team P joined team Q, and 10% of girls from team Q joined team P, what percentage are the girls in team Q of the girls in team P?

**Options:**

Accepted Answer

**Solution:**

1. Let the number of girls in class B be *x*.
   - Then boys in B = *x + 20*.

2. Number of girls in class C = girls in B + 20% of girls in B = *x + 0.2x = 1.2x*.
   Number of boys in class C = boys in B + 20% of boys in B = *(x + 20) + 0.2(x + 20) = 1.2(x + 20)*.

3. Girls in team P = 60% of girls in classes B and C combined:
   $$\text{Girls in P} = 0.6 \times (x + 1.2x) = 0.6 \times 2.2x = 1.32x$$

4. Boys in team P is 13 less than girls in team P:
   $$\text{Boys in P} = 1.32x - 13$$

5. Boys in team P is also 50% of boys in classes A and C combined.
   Let girls in A be *g_A*, then boys in A = *g_A + x*.
   Total boys in A and C = boys in A + boys in C = *(g_A + x) + 1.2(x + 20)*.
   Since boys in P = 50% of this total:
   $$1.32x - 13 = 0.5 \times \left[(g_A + x) + 1.2(x + 20)\right]$$

(Note: *g_A* is not needed to find the required percentage as it cancels out in the ratio.)

6. The ratio of girls in team P to girls in team Q is 3:4.
   So, if girls in P = 3k, girls in Q = 4k.

7. After 30% of girls in team P move to team Q, and 10% of girls in team Q move to team P:
   - Girls remaining in P = 70% of girls in P + 10% of girls in Q = 0.7 $\times $3k + 0.1 $\times$ 4k = 2.1k + 0.4k = 2.5k
   - Girls in Q after transfer = 90% of girls in Q + 30% of girls in P = 0.9 $\times$ 4k + 0.3 $\times$ 3k = 3.6k + 0.9k = 4.5k

8. Required percentage = $$ \frac{\text{Girls in Q after transfer}}{\text{Girls in P after transfer}} \times 100 = \frac{4.5k}{2.5k} \times 100 = 180\% $$

**Answer:** 180\%

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