Question

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?

A. 22(2/9)%B. 16(2/3)%C. 11(1/9)%D. 10%E. 5%

Answer 1

option D

Explanation:

Assume number of bulb in the hostel be 100

number of bulb on at 8 p.m.

= 80 % of total bulb

= 0.8 x 100 = 80 bulb

Let L be the number of light on and 100 - L be the light that are off

now,

Light on = 40 % of (100 - L) + 90 % of L

80 = 40 - 0.4 L + 0.9 L

40 = 0.5 L

L = 80 bulb

number of bulbs which were off = 100-80 = 20 bulb

number of bulbs that are on are supposed to be off = 40 % of 20

= 0.4 x 20 = 8 bulbs

percentage =
`(8)/(80)}* 100`

= 10 %

Hence, the correct answer is option D