A library had picture books and atlases. At first, the ratio of the number of picture books to the number of atlases was 5 : 6. The librarian lent out 10 picture books and bought 15 more atlases. After this, the ratio of the number of picture books to the number of atlases became 2 : 3. How many books were there in the library at first?
- 100
- 120
- 220
- 250
Need a hint?
Write the first ratio using one unknown part, then use the new ratio to find the value of that part before you add the two amounts.
Worked answer
- Let 1 part be u. At first, picture books = 5u and atlases = 6u.
- After the change: picture books = 5u − 10 and atlases = 6u + 15.
- The new ratio is 2 : 3, so 3 × (5u − 10) = 2 × (6u + 15).
- 15u − 30 = 12u + 30, so 3u = 60 and u = 20.
- At first there were 5 × 20 = 100 picture books and 6 × 20 = 120 atlases.
- Total at first = 100 + 120 = 220 books.
Answer: 220 books
The mistake this question tests
Habit
Stopped at one part in ratio
Many pupils stop after finding one type of book, or add the numbers after the change instead of the numbers at first.
How to fix it at home →More PSLE ratio questions
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See the answer →Practise PSLE ratio until the mistakes stop.
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