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50% of the apartments in a certain building have windows and hardwoods floors. 25% of the apartments without Windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what percent of the apartments with Windows ha e hardwood floors?

A 10%
B 16.66%
C 40%
D 50%
E 83.33%

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vaibhav101 wrote:
50% of the apartments in a certain building have windows and hardwoods floors. 25% of the apartments without Windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what percent of the apartments with Windows ha e hardwood floors?

A 10%
B 16.66%
C 40%
D 50%
E 83.33%
We can let the total number of apartments = 100.

So, 50 have windows and hardwood floors.

Since 40 do not have hardwood floors, then 60 do have hardwood floors.

Thus, 60 - 50 = 10 have hardwood floors but no windows.

We are given that 25% of the apartments without windows have hardwood floors and we found the number of such apartments is 10. If 25% of the apartments without windows is 10, the total number of apartments without windows is 10/0.25 = 40. Thus, there are 100 - 40 = 60 apartments that have windows.

Since 50 of them have hardwood floors, 50/60 = ⅚ = 83.33% of them have hardwood floors.

Answer: E

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Let a = total window
b = total of apartment with no window.
Apartment with window and hardwood floor = 50%
$$=\ \frac{50}{100}=\ 0.5$$
$$Apartments\ without\ window\ bat\ have\ hardwood\ floor\ =25\%\ =\ \frac{25}{100\ }=\ 0.25$$

$$Apartments\ without\ hardwood\ floor\ =40\%\ =\ \frac{40}{100\ }=\ 0.4$$
Proportion of apartment with windows = a - b
1 - 0.4 = 0.6
$$\leftDesire\ proprtion\ =\ \frac{\left(Apartment\ with\ windows\ \&\ hardwood\ \right)}{total\ windows}\ \right\cdot\frac{100}{1}$$
$$=\ \frac{0.5}{0.6}\ \cdot\ \frac{100}{1}$$
= 83.33%
Option E is CORRECT.

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