The ratio of the number of fiction books to non-fiction books to dictionaries was 2: 5: 4. After a librarian bought another 68 books of each type, the new ratio became 23 : 32 : 29. How many dictionaries were there at first? A. 16 B. 14 C. 12 D. 48
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ans c
explanation
Let the no offiction books, nonfiction books and dictionaries be 2x, 5x 4x and the no after buying 68 books of each type be 23y, 32y, 29y respectively. From the given data we obtain 3 equations :-
1. 2x + 68 = 23y
2. 5x + 68 = 32y
3. 4x + 68 = 29y
ON SUBTRACTING EQUATION 3 FROM EQUATION 2 WE OBTAIN:-
x = 3y
USING THIS VALUE IN EQUATION 1 WE GET
y = 4 and thus x = 3y = 12.
no of dictionaries = 4x =48(the correct option is c)
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