The number of fiction books at a library was 3/4 of the total number of books. After 592 fiction books were DONATED TO THE LIBRARY, the number of fiction books became 5/6 of the total number of books. How many books were there at the library at first?
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Question
Answer
Method 1 :
total number of books at first : 4 units
number of fiction books —
at first : 3 units
after : 5 units
5 units – 3 units = 2 units = 592
4 units = 2 x 592 = 1184
Method 2 :
fiction books : total number of books
3u : 4u (before donation)
5p : 6p (after donation)
3u + 592 ——- 5p
18u + 3552 ——- 30p
4u + 592 ——- 6p
20u + 2960 ——- 30p
20u + 2960 ——- 18u + 3552
20u – 18u = 2u ——- 3552 – 2960 = 592
1u ——- 592/2 = 296
4u ——- 296 x 4 = 1184
Ans : 1184 books.
Using Model drawing.
I would solve the above question as follows :
ficton books : total number of books
3u : 4u (before donation)
5p : 6p (after donation)
3u + 592 ——- 5p
18u + 3552 ——- 30p
4u + 592 ——- 6p
20u + 2960 ——- 30p
20u + 2960 ——- 18u + 3552
20u – 18u = 2u ——- 3552 – 2960 = 592
1u ——- 592/2 = 296
4u ——- 296 x 4 = 1184
Ans : 1184 books.