A library shelf held some fiction books and some non-fiction books. In the morning, 40 non-fiction books were added to the shelf and the ratio of fiction books to non-fiction books became 5 : 4. Then 60 fiction books were taken off the shelf and the ratio became 1 : 2. (a) How many fiction books were on the shelf at first? (b) In the afternoon, more books were added. The number of fiction books increased by 150% and the number of non-fiction books increased by 25%. Find the total number of books added to the shelf in the afternoon.

RatioStructured · 5 marks

A library shelf held some fiction books and some non-fiction books. In the morning, 40 non-fiction books were added to the shelf and the ratio of fiction books to non-fiction books became 5 : 4. Then 60 fiction books were taken off the shelf and the ratio became 1 : 2.

How many fiction books were on the shelf at first?
In the afternoon, more books were added. The number of fiction books increased by 150% and the number of non-fiction books increased by 25%. Find the total number of books added to the shelf in the afternoon.

Need a hint?

For (a), find how many units the fiction books are after the removal, using the new ratio 1 : 2 and the fact that non-fiction stayed at 4 units. For (b), take each percentage of the number at the start of the afternoon, not of the number at first.

Worked answer

(a) After the 40 books were added: fiction : non-fiction = 5 : 4, so fiction = 5 units and non-fiction = 4 units.
(a) After 60 fiction books were removed the ratio is 1 : 2. Non-fiction is still 4 units, so 4 units = 2 parts, meaning 1 part = 2 units and fiction = 2 units.
(a) Fiction removed: 5 units − 2 units = 3 units = 60 books, so 1 unit = 20 books.
(a) Fiction at first = 5 units = 100 books.
(b) At the start of the afternoon: fiction = 2 units = 40 books, non-fiction = 4 units = 80 books.
(b) Fiction increase: 150% of 40 = 60 books.
(b) Non-fiction increase: 25% of 80 = 20 books.
(b) Total added = 60 + 20 = 80 books.

Answer: 80 books

The mistake this question tests

Habit

Percentage of a new total

Many pupils take 150% and 25% of the original numbers from the start of the morning, or forget to add both increases together, which gives a wrong total.

How to fix it at home →

A library shelf held some fiction books and some non-fiction books. In the morning, 40 non-fiction books were added to the shelf and the ratio of fiction books to non-fiction books became 5 : 4. Then 60 fiction books were taken off the shelf and the ratio became 1 : 2.

Worked answer

The mistake this question tests

Percentage of a new total

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