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

- Hostel A has 120 boys. The number of girls in A is 30\% more than the number of girls in hostel B.
- Hostel B has boys twice the number of girls.
- Hostel C has 100 more boys than hostel A, and the total number of boys and girls in 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:** What percent more is the total number of boys in hostel A and girls in hostel C compared to the number of boys in hostel B?

Question

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

- Hostel A has 120 boys. The number of girls in A is 30\% more than the number of girls in hostel B.
- Hostel B has boys twice the number of girls.
- Hostel C has 100 more boys than hostel A, and the total number of boys and girls in 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:** What percent more is the total number of boys in hostel A and girls in hostel C compared to the number of boys in hostel B?

Accepted Answer

**Solution:**

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

2. Boys in hostel B = twice the number of girls = $2x$.

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

4. Boys in hostel A = 120 (given).

5. Boys in hostel D = Boys in A + 182 = $120 + 182 = 302$.

6. Boys in hostel D are 98 less than boys in B:
   $$ 302 = 2x - 98 \implies 2x = 400 \implies x = 200 $$

7. Girls in hostel B = $x = 200$.

8. Girls in hostel A = $1.3 \times 200 = 260$.

9. Average girls in A and D = 223:
   $$ \frac{260 + \text{Girls in D}}{2} = 223 \implies \text{Girls in D} = 2 \times 223 - 260 = 186 $$

10. Boys in hostel C = Boys in A + 100 = $120 + 100 = 220$.

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

12. Total boys in A and girls in C = $120 + 780 = 900$.

13. Number of boys in B = $2x = 400$.

14. Required percentage increase:
    $$
    \frac{900 - 400}{400} \times 100 = \frac{500}{400} \times 100 = 125\% 
    $$

**Answer:** 125\%

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