In an album, football cards made up 40% of all the cards. Then 60 more basketball cards were added. Now football cards made up 25% of all the cards. How many football cards were in the album?
2 units = 2 × 20 = 40 cards
Ans: 40
How to solve it
Find the quantity that does not change: the football cards. Only basketball cards are added.
Draw the album before: football is 40 percent and basketball 60 percent, which cuts down to 2 units and 3 units.
Draw the album after: football is 25 percent and basketball 75 percent, so the ratio is 1 to 3.
Make the football units match. Multiply both sides by 2: 1 to 3 becomes 2 to 6, so football is 2 units in both.
The extra 3 units are the 60 cards added, so 1 unit is 20 and football, 2 units, is 40 cards.
The football cards never changed. Their share fell from 40 percent to 25 percent only because the total grew.
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 · Intermediate · free to tryA shop had silver and gold balloons. Silver balloons made up 75% of the…A shop had silver and gold…
A shop had silver and gold balloons. Silver balloons made up 75% of the balloons. The shop bought some gold balloons, and silver balloons then made up 60% of the balloons. The shop then bought 60 more gold balloons, and silver balloons made up 50% of the balloons. How many silver balloons were there?
the silver balloons never changed, only gold balloons were bought
at first, silver = 75% = 75/100 = 3/4 of the balloons
after the first buy, silver = 60% = 60/100 = 3/5 of the balloons
in the end, silver = 50% = 50/100 = 3/6 of the balloons
silver balloons = 3 units at every stage
balloons at first = 4 units
balloons after the first buy = 5 units
balloons in the end = 6 units
the second buy = 6 units − 5 units = 1 unit
1 unit = 60
3 units = 3 × 60 = 180 silver balloons
Answer: 180
For parents
How do you solve P6 percentage questions with an unchanged quantity?
In these before-and-after questions one amount stays fixed while the total grows or shrinks, so its percentage share moves.
What your child learns here
In these before-and-after questions one amount stays fixed while the total grows or shrinks, so its percentage share moves. Your child learns to change each percentage into a ratio, match the units of the unchanged amount, and count.
Write a percentage share as a ratio of the parts, such as 40% and 60% as 2 : 3.
Find the quantity that does not change, and make its units the same in both ratios.
Use the change in units to find 1 unit, then the amount asked for.
Applies finding the whole and the link between fraction and ratio to multi-step problems.
Does the answer make sense?
The fixed amount is a smaller share of a bigger total, so if its percentage falls, the total must have grown, and if its percentage rises, the total must have shrunk. Your child can match this to the story: gold balloons bought means more in all, papayas sold means fewer.
How to practise these questions
The Intermediate questions train finding the quantity that stays the same while percentages shift, sometimes a total, sometimes a sum of two kinds, sometimes across three stages. If the quantity that stays is hard to find, read the written step-by-step solution.
Questions parents ask
What is the difference between 'increased to' and 'increased by'? 'Increased to 60%' gives the new percentage. 'Increased by 60%' gives the change, so the new amount is 160% of the old. The small word decides the whole method.
Why change percentages into ratios in these questions? A percentage share is a part of the total, and here the total changes. Writing each share as a ratio, such as 40% and 60% as 2 : 3, lets your child match the unchanged quantity in units.
Which syllabus outcomes does an unchanged quantity question use? It uses Primary 6 percentage outcome 1.1, finding the whole given a part and the percentage, together with ratio outcome 1.7, the relationship between fraction and ratio.
