Number of books of the first category: the number of other three categories = 1: 2, and the number of books of the first category accounts for1(1+2) =1/3 of the number of books of the four categories;

Number of second-class books: the number of other three-class books = 1: 3, and the number of second-class books accounts for1/(1+3) =1/4;

Number of books of the third category: the number of other three categories = 1: 4, and the number of books of the third category accounts for1(1+4) =1/5 of the number of books of the fourth category;

Then, the proportion of books of the fourth category is1-1/3-1/4-1/5 =13/60.

Number of books in four categories =26÷ 13/60= 120.

2. The burning speed of thin candle is the burning speed of thick candle;

(2/ 1)÷( 1/2)=4 times

For the same length, the burning time of a thin candle is 1/4 of that of a thick candle.

It turns out that thick candles can burn more than thin candles: 2- 1= 1 hour.

Aft burning for that same time,

The remaining thick candles can burn more than the thin candles 1 hour.

The remaining thick candles can still burn;

1÷ (1-1/4) = 4/3 hours

Power outage time: 2-4/3=2/3 hours.