The table below shows five colleges with five departments each: Arts, Commerce, Medical, Science, and Vocational. For each department, the total number of applications received, the percentage of canceled applications (male + female), and the ratio of male to female in approved applications are given.

| Department | Total Applications Received | Percentage of Canceled Applications | Ratio of Male : Female (Approved) |
|------------|-----------------------------|------------------------------------|-----------------------------------|
| Arts | P | 40\% | 11 : 7 |
| Commerce | 1400 | Q | 29 : 21 |
| Medical | 1600 | 35\% | R |
| Science | S | 55\% | 43 : 17 |
| Vocational | 800 | 60\% | T |

If the difference between approved male and approved female applications in the Arts department is 200, then find how much percent more is P than the applications received in the Vocational department.

Question

The table below shows five colleges with five departments each: Arts, Commerce, Medical, Science, and Vocational. For each department, the total number of applications received, the percentage of canceled applications (male + female), and the ratio of male to female in approved applications are given.

| Department | Total Applications Received | Percentage of Canceled Applications | Ratio of Male : Female (Approved) |
|------------|-----------------------------|------------------------------------|-----------------------------------|
| Arts       | P                           | 40\%                              | 11 : 7                            |
| Commerce   | 1400                        | Q                                 | 29 : 21                          |
| Medical    | 1600                        | 35\%                              | R                                |
| Science    | S                           | 55\%                              | 43 : 17                          |
| Vocational | 800                         | 60\%                              | T                                |

If the difference between approved male and approved female applications in the Arts department is 200, then find how much percent more is P than the applications received in the Vocational department.

Accepted Answer

**Solution:**

1. Let the total applications received in Arts department be *P*.

2. Percentage of canceled applications in Arts = 40\%, so approved applications = 60\% of *P* = $0.6P$.

3. The ratio of approved male to female applications in Arts is 11:7.

4. Let the approved male applications be $11x$ and approved female applications be $7x$.

5. Total approved applications = $11x + 7x = 18x$.

6. Since total approved applications = $0.6P$, we have:
   $$ 18x = 0.6P \implies x = \frac{0.6P}{18} = \frac{P}{30} $$

7. The difference between approved male and female applications is given as 200:
   $$ 11x - 7x = 4x = 200 \implies x = 50 $$

8. From step 6 and 7, equate $x$:
   $$ \frac{P}{30} = 50 \implies P = 1500 $$

9. Applications received in Vocational department = 800.

10. Find how much percent *P* is more than 800:
    $$
    \text{Percentage increase} = \frac{P - 800}{800} \times 100 = \frac{1500 - 800}{800} \times 100 = \frac{700}{800} \times 100 = 87.5\% 
    $$

**Answer:** 87.5\%

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