The table below shows the ratio of employees registered for eye checkup to those registered for dental checkup in four different time slots (A, B, C, and D) in a company.

| Time slots | Ratio of employees registered for Eye checkup to Dental checkup |
|------------|-----------------------------------------------------------------|
| A | 5:4 |
| B | 7:3 |
| C | 11:4 |
| D | 1:5 |

Note: Employees registered are either for eye checkup or for dental checkup.

If the total number of employees in the company is $880$ and $9\frac{1}{11}\%$ of the total employees registered in slot B is $220$, find the difference between the number of employees registered for dental checkup and those registered for eye checkup in slot B.

Question

The table below shows the ratio of employees registered for eye checkup to those registered for dental checkup in four different time slots (A, B, C, and D) in a company.

| Time slots | Ratio of employees registered for Eye checkup to Dental checkup |
|------------|-----------------------------------------------------------------|
| A          | 5:4                                                             |
| B          | 7:3                                                             |
| C          | 11:4                                                            |
| D          | 1:5                                                             |

Note: Employees registered are either for eye checkup or for dental checkup.

If the total number of employees in the company is $880$ and $9\frac{1}{11}\%$ of the total employees registered in slot B is $220$, find the difference between the number of employees registered for dental checkup and those registered for eye checkup in slot B.

Accepted Answer

**Solution:**

1. First, calculate the number of employees registered in slot B.
   - Given that $9\frac{1}{11}\%$ of the total employees are registered in slot B.
   - Convert $9\frac{1}{11}\%$ to an improper fraction: $9\frac{1}{11} = \frac{100}{11}\% = \frac{100}{11} 	imes \frac{1}{100} = \frac{1}{11}$.
   - Total employees = $880$.
   - Employees registered in slot B = $880 	imes \frac{1}{11} = 80$.

2. The ratio of employees registered for eye checkup to dental checkup in slot B is $7:3$.
   - Total parts = $7 + 3 = 10$.
   - Number of employees for eye checkup = $\frac{7}{10} 	imes 80 = 56$.
   - Number of employees for dental checkup = $\frac{3}{10} 	imes 80 = 24$.

3. Find the difference between employees registered for dental checkup and eye checkup:
   $$|24 - 56| = 32$$

**Answer:** $32$

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