The table below shows data for five departments across various colleges: total applications received, percentage of canceled applications, and the ratio of approved male to female applications.

| Department | Total Applications Received | Percentage of Canceled Applications | Ratio of Approved Male : Female |
|-------------|-----------------------------|------------------------------------|---------------------------------|
| 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 number of approved male applications in the Vocational department is 40 more than the number of approved female applications, what is the ratio of approved female applications to approved male applications in the Vocational department?

Question

The table below shows data for five departments across various colleges: total applications received, percentage of canceled applications, and the ratio of approved male to female applications.

| Department  | Total Applications Received | Percentage of Canceled Applications | Ratio of Approved Male : Female |
|-------------|-----------------------------|------------------------------------|---------------------------------|
| 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 number of approved male applications in the Vocational department is 40 more than the number of approved female applications, what is the ratio of approved female applications to approved male applications in the Vocational department?

Accepted Answer

**Solution:**

1. Total applications received in Vocational department = 800

2. Percentage of canceled applications = 60\%

3. Therefore, approved applications = 40\% of 800 = $ \frac{40}{100} \times 800 = 320 $

4. Let the number of approved female applications be *x*.

5. Number of approved male applications = *x + 40* (given)

6. Total approved applications = male + female = *x + (x + 40) = 2x + 40*

7. From step 3, total approved applications = 320, so:

$$2x + 40 = 320$$

$$2x = 280$$

$$x = 140$$

8. Approved female applications = 140

9. Approved male applications = 140 + 40 = 180

10. Required ratio of approved female to approved male applications:

$$\frac{140}{180} = \frac{7}{9}$$

11. However, the ratio given in options is in the form female : male, so ratio is 7 : 9.

**But note:** The question asks for the ratio of approved female to approved male applications in the Vocational department, and the options include 7 : 9 and 5 : 7, etc. Our calculation shows 7 : 9.

**Re-examining the options:**
- Option (d) is 7 : 9
- Option (b) is 5 : 7

Since our calculation yields 7 : 9, the correct answer is option (d).

**Answer:** 7 : 9

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