There are four hostels: A, B, C, and D.

- Hostel A has 120 boys and the number of girls is 30\% more than the number of girls in hostel B.
- In hostel B, the number of boys is double the number of girls.
- Hostel C has 100 more boys than hostel A, and the total number of boys and girls in hostel C is 1000.
- Hostel D has 182 more boys than hostel A. The average number of girls in hostels A and D is 223. The number of boys in hostel D is 98 less than the number of boys in hostel B.

**Question:** If 20 boys leave from each hostel, what is the average number of boys remaining in all the hostels?

Question

There are four hostels: A, B, C, and D.

- Hostel A has 120 boys and the number of girls is 30\% more than the number of girls in hostel B.
- In hostel B, the number of boys is double the number of girls.
- Hostel C has 100 more boys than hostel A, and the total number of boys and girls in hostel C is 1000.
- Hostel D has 182 more boys than hostel A. The average number of girls in hostels A and D is 223. The number of boys in hostel D is 98 less than the number of boys in hostel B.

**Question:** If 20 boys leave from each hostel, what is the average number of boys remaining in all the hostels?

Accepted Answer

**Solution:**

1. Let the number of girls in hostel B be $x$.

2. Number of girls in hostel A = 30\% more than girls in B = $x + 0.3x = 1.3x$.

3. Number of boys in hostel B = double the girls in B = $2x$.

4. Number of boys in hostel A = 120 (given).

5. Number of boys in hostel C = boys in A + 100 = $120 + 100 = 220$.

6. Total boys and girls in hostel C = 1000, so girls in C = $1000 - 220 = 780$.

7. Number of boys in hostel D = boys in A + 182 = $120 + 182 = 302$.

8. Average number of girls in A and D = 223, so
   $$
   \frac{\text{girls in A} + \text{girls in D}}{2} = 223 \implies \text{girls in A} + \text{girls in D} = 446
   $$

9. Girls in A = $1.3x$, so girls in D = $446 - 1.3x$.

10. Number of boys in hostel D is 98 less than boys in B:
    $$
    \text{boys in D} = \text{boys in B} - 98 \implies 302 = 2x - 98 \implies 2x = 400 \implies x = 200
    $$

11. Now, girls in B = $x = 200$, girls in A = $1.3 \times 200 = 260$, girls in D = $446 - 260 = 186$.

12. Boys in B = $2x = 400$, boys in A = 120, boys in C = 220, boys in D = 302.

13. After 20 boys leave from each hostel:
    - Boys in A = $120 - 20 = 100$
    - Boys in B = $400 - 20 = 380$
    - Boys in C = $220 - 20 = 200$
    - Boys in D = $302 - 20 = 282$

14. Average number of boys remaining:
    $$
    \frac{100 + 380 + 200 + 282}{4} = \frac{962}{4} = 240.5
    $$

**Answer:** 240.5

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