hotel california lights question

[semidevil]

Here is the problem:. see my thought process below and let me know where I went wrong:

Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off?


Im not good at using matrix, so this is what I did:

-start with 100 lights.
-80% of lights switched on ==> 80 lights are switched on, 20 lights are off.
-40% of the lights that are supposed to be off are actually on. ==> out of 80 lights on, 32 are supposed to be off, but are on.
- 10% of the lights that are supposed to be swtiched on are actually off. ==> 10% of 20 ==> 4 lights.

Question: what % of lights are switched on are supposed to be switched off?

Why is it not 32%. 32/100?

answer is 16 and 2/3%.

[kapsii]

There is another thread on the same question at the link below... better if you check it for solution.

https://www.beatthegmat.com/lights-in-a- ... tml#138417

As far as where you went wrong in your logic...

40% of the lights that are supposed to be off are actually on. ==> out of 80 lights on, 32 are supposed to be off, but are on.

The question contains two unknown factors, the number/percentage of lights which were SUPPOSED to be ON and the number of lights which were SUPPOSED to be OFF.
So, when you deduced that 32 lights are SUPPOSED to be off but are ACTUALLY on, you calculated 40% of the lights which are ACTUALLY ON...
Thus your answer is not correct... and btw, I think the OA that you mentioned is not correct too...