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

- In hostel A, the number of boys is 120, 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.
- In hostel C, the number of boys is 100 more than the number of boys in hostel A, and the total number of boys and girls is 1000.
- In hostel D, the number of boys is 182 more than the number of boys in 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:** Find the difference between the total number of boys and girls together in hostel A and that in hostel D.

Question

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

- In hostel A, the number of boys is 120, 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.
- In hostel C, the number of boys is 100 more than the number of boys in hostel A, and the total number of boys and girls is 1000.
- In hostel D, the number of boys is 182 more than the number of boys in 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:** Find the difference between the total number of boys and girls together in hostel A and that in hostel D.

Accepted Answer

**Solution:**

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

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

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

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

9. Now, girls in B = $x = 200$.

10. Girls in A = $1.3 \times 200 = 260$.

11. Average number of girls in A and D is 223:
    $$ \frac{260 + \text{girls in D}}{2} = 223 \implies 260 + \text{girls in D} = 446 \implies \text{girls in D} = 186 $$

12. Total boys and girls in A = $120 + 260 = 380$.

13. Total boys and girls in D = $302 + 186 = 488$.

14. Required difference = total in D - total in A = $488 - 380 = 108$.

**Answer:** 108

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