The ratio of comic books to storybooks on a shelf was 2 : 5. After 18 more comic books were added, the ratio became 4 : 5. How many storybooks are on the shelf?
There are 45 storybooks.
Ans: 45
How to solve it
Draw the first ratio: comic books 2 units and storybooks 5 units.
Look for the quantity nobody touches. Only comic books are added, so the storybooks stay the same.
Line the ratios up: 2 to 5 before and 4 to 5 after. The storybooks are 5 units in both, so the units match.
The comic books grew from 2 units to 4 units, so the 18 new comic books are 2 units.
Find 1 unit: half of 18 is 9. The storybooks are 5 units, and 5 times 9 is 45.
The storybooks never changed. That's what made the units match.
Practice questions with worked solutions
Question 1 is free to try. The other 7 open in the free trial, each with its full working.
Question 1 of 8 · Basic · free to tryThe number of chess sets to the number of jigsaw puzzles in a cupboard was…The number of chess sets to the…
The number of chess sets to the number of jigsaw puzzles in a cupboard was in the ratio 6 : 5. After 40 jigsaw puzzles were given away, the ratio became 6 : 1. How many chess sets are in the cupboard?
How do you solve P6 ratio questions with one quantity unchanged?
Here one quantity is added to or taken from, and the other is left alone.
What your child learns here
Here one quantity is added to or taken from, and the other is left alone. Your child learns to find the quantity nobody touched and to make its units match, so the change can be read straight from the bars.
Identify the quantity that stays the same in a before-and-after story.
Rewrite both ratios so that quantity has the same number of units in each.
Read the change as the difference in units of the other quantity, and find 1 unit.
Applies equivalent ratios and missing terms to word problems.
Does the answer make sense?
Your child should find that the quantity nobody touched, such as the orchids or the storybooks, comes out as the same number before and after. The quantity that was added to must end up larger than it started, and one that lost some, like the durian puffs sold, must end up smaller.
How to practise these questions
The Basic questions train spotting the quantity that does not change and making its units match before and after. Intermediate questions use the same idea with more steps. Challenge questions hide the unchanged quantity more deeply inside the story. When the unchanged quantity is hard to spot, read the written step-by-step solution.
Questions parents ask
How do I know which quantity stays the same? Read what the story does. If only one kind is added, sold or given away, the other kind is untouched, and that untouched quantity is the one to match.
Why can't my child compare the two ratios straight away? Units in two different ratios are not the same size unless one quantity matches. Rewriting both ratios so the unchanged quantity has the same number of units makes every unit worth the same.
Does my child need the lowest common multiple for this? Yes, when the unchanged quantity has different numbers in the two ratios. Both ratios are multiplied so that quantity reaches a common multiple, and this page writes 'lowest common multiple' in full rather than a short form.
