The table below shows the number of flats occupied by public sector employees in four different buildings, the ratio of flats occupied by public sector to private sector employees, and the percentage of vacant flats. The total flats in each building equal the sum of occupied and vacant flats.

| Buildings | Flats occupied by public sector employees | Ratio of flats occupied by public sector to private sector employees | Percentage of vacant flats |
|:---------:|:------------------------------------------:|:---------------------------------------------------------------:|:--------------------------:|
| A | $4x + 40$ | $2:1$ | $40\%$ |
| B | $240$ | $8:5$ | $25\%$ |
| C | $300$ | $5:3$ | $20\%$ |
| D | $150$ | $2:1$ | $55\%$ |

It is given that the number of flats in a floor is $2.5x$ and the number of flats on each floor is the same for all buildings.

**Question:** What is the sum of the number of floors in buildings C and D?

Question

The table below shows the number of flats occupied by public sector employees in four different buildings, the ratio of flats occupied by public sector to private sector employees, and the percentage of vacant flats. The total flats in each building equal the sum of occupied and vacant flats.

| Buildings | Flats occupied by public sector employees | Ratio of flats occupied by public sector to private sector employees | Percentage of vacant flats |
|:---------:|:------------------------------------------:|:---------------------------------------------------------------:|:--------------------------:|
| A         | $4x + 40$                                | $2:1$                                                           | $40\%$                    |
| B         | $240$                                    | $8:5$                                                           | $25\%$                    |
| C         | $300$                                    | $5:3$                                                           | $20\%$                    |
| D         | $150$                                    | $2:1$                                                           | $55\%$                    |

It is given that the number of flats in a floor is $2.5x$ and the number of flats on each floor is the same for all buildings.

**Question:** What is the sum of the number of floors in buildings C and D?

Accepted Answer

**Solution:**

1. Given that the number of flats in a floor is $2.5x$ and flats per floor are the same for all buildings.

2. From building A, flats occupied by public sector employees are $4x + 40$ and the ratio of public to private sector flats is $2:1$.

3. Total flats occupied in building A are given as 300. Since the ratio is $2:1$, total occupied flats = public + private = $2m + m = 3m$.

4. Using the ratio and occupied flats, we find the total flats in building A:
   - Public flats = $4x + 40$
   - Total occupied flats = 300
   - So, $4x + 40 = 2m$ and $m = \frac{4x + 40}{2}$
   - Total occupied flats = $3m = 300$ implies $3 	imes \frac{4x + 40}{2} = 300$
   - Simplifying: $\frac{3}{2} (4x + 40) = 300$  
   - $3(4x + 40) = 600$  
   - $12x + 120 = 600$  
   - $12x = 480$  
   - $x = 40$

5. Flats per floor = $2.5x = 2.5 	imes 40 = 100$

6. Calculate total flats in buildings C and D:
   - Building C: Vacant flats = 20% of total flats, so occupied flats = 80%.
     Occupied flats = 300 (public) + private flats.
     Ratio public:private = 5:3, so total occupied flats = $300 	imes \frac{8}{5} = 480$.
     Total flats in C = $\frac{480}{0.8} = 600$.

- Building D: Vacant flats = 55%, so occupied flats = 45%.
     Occupied flats = 150 (public) + private flats.
     Ratio public:private = 2:1, so total occupied flats = $150 	imes \frac{3}{2} = 225$.
     Total flats in D = $\frac{225}{0.45} = 500$.

7. Number of floors in C = $\frac{600}{100} = 6$.

8. Number of floors in D = $\frac{500}{100} = 5$.

9. Sum of floors in C and D = $6 + 5 = 11$.

**Answer:** 11

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