let a% be the lights to be switched on = a %
then lights to be switched off = (100-a) %

total percent of lights switched on is 80. which come on RHS

40% of lights supposed to be off ( 100-a)% are actually on = 0.4(100-a)
also 10% of lights supposed to be on are actually off , so 0.1(a) these are off , so remaining to be on = a - 0.1a

now total lights on = 80
0.4(100-a) + (a-.1a) = 80
a=80 should be on

% of lights supposed to be off are on = 0.4(100-a) / 80 x100
= 0.4x2x100/80
=10%

Ans is D

hey,
i dont understand how you got step 4, can you please clarify on it? thanks!

Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?
-------
Correct me if my logic is wrong
------
According to my simple thinking without calculation
Background: 80% light is on-->20% light is off.
Target question: % lights that are on are supposed to be off
Actual:
+40% off when it is supposed to be on-->this belongs to 20% light is off
+10% on when it is supposed to be off-->this belongs to 80% light is on
My answer is D (10%) since it perfectly matches my analysis.
-----
Since the question asks for % instead of actual number so I don't calculate or assume in actual numbers and go back to % as a conclusion.
If it has to be in actual numbers, it should be:
In 100 lights, there's 80 lights that are on, 20 lights that are off.
+40% off when it is supposed to be on-->this belongs to 20% light is off--->40% out of 20% category means 40% in 20 lights, and it equals to 8 lights.
+10% on when it is supposed to be off-->this belongs to 80% light is on--->10% in 80 lights, and it equals to 8 lights.
Percent of the lights that are on are supposed to be off-->(8/80)*100%= 10% (8 is extracted from 10% on when it is supposed to be off)