valaparla wrote:

Eighty percent of the lights at Hotel California are on at 8pm a certain evening. However, forty percent of the lights that are supposed to 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?

A) 22 2/9%

B) 16 2/3%

C) 11 1/9%

D) 10%

E) 5%

Is the Answer D.

let me try..

Let the light which are supposed to be OFF = SO

Let the light which are supposed to be ON = SN

Let the light which are ACTUALLY OFF = AO

Let the light which are ACTUALLY ON = AN

Let the total no. of lights be 100,

So ACTUALLY ON lights = 80

And ACTUALLY OFF lights = 20

Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON

it means >>> (60/100)*SO are ACTUALLY OFF

Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF

it means >>> (90/100)*SN are ACTUALLY ON

So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80

and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80

From here we get SO = 20

we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.

So (8/80)*100 = 10%

OA plz.