Find the fraction

Question

A class was given a book to read. 1/4 of the students didn’t read it. Of the students who did, 3/5 were boys. Of the students who didn’t read the book 2/5 were girls. What fraction of the class were girls? 

Answer 1

1/4 of the students did not read the book.

2/5 * 1/4 of the students were girls who did not read the book, so 2/20 = 1/10

of the total student body were girls who did not read the book.

Then 1/4 - 1/10 = 6/40 = 3/20 were boys who did not read the book.

3/20 + 1/10 = 3/20 + 2/20 = 5/20 = 1/4

3/5 * 3/4 = 9/20 were boys who read the book.

3/4 - 9/20 = 15/20 - 9/20 = 6/20 = 3/10 were girls read the book.

# of girls is 1/10 + 3/10 = 4/10 = 2/5 of the class are girls.

The following table summarizes

BOYS GIRLS TOTAL

read 9/20 3/10 15/20 = 3/4

did not read 3/20 1/10 5/20 = 1/4

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TOTAL 12/20=3/5 2/5 1