alimad wrote:
Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book?
A. 1/10
B. 3/20
C. 1/5
D. 1/4
E. 9/20
We know that M = 2P
P = 4 + C
M = 8+2C
8 + 2c + 4 + c + c = 20
4c + 12 = 20
4c = 8
c = 2 , P = 6, M = 12
Please assist further. Thanks
Solution:Since 20% of the shelf is empty, 80% is full and thus, there are 25 x 0.8 = 20 books on the shelf.
Let c denote the number of chemistry books. Then, there are c + 4 physics books and 2(c + 4) = 2c + 8 mathematics books. Since the sum of the books on the three subjects is 20, we have:
c + (c + 4) + (2c + 8) = 20
4c + 12 = 20
4c = 8
c = 2
Thus, there are 2 chemistry books, c + 4 = 6 physics books and 2c + 8 = 12 mathematics books.
Since there are 12 soft cover books, the number of books that are hard cover is 20 - 12 = 8. Since 7 of these hard cover books is either a mathematics book or a physics book, it follows that there is 8 - 7 = 1 hard cover book on chemistry.
The condition “a book selected at random is either a hard cover book or a chemistry book” is satisfied if the selected book is one of the 8 hard cover books, or if it is the only soft cover chemistry book. Thus, 8 + 1 = 9 books satisfy this condition. Therefore, the required probability is 9/20.
Answer: E