Ratios & Proportional Reasoning
Dr. Davinder Bhachu & Nick Featherstone
Teachers
Contents
Introduction - Ratios & Proportional Reasoning
What are ratios?
Ratios tell you how many parts of one item exist relative to parts of another item.
Example
The class has 12 boys and 8 girls.
Ratio of boys to girls
This means for every 3 boys, there are 2 girls.
Why are ratios & proportional reasoning tested in the UCAT?
Tests your ability to quickly interpret and apply numerical data in real-life scenarios.
Assesses how well you can simplify, compare, and use ratios under time pressure.
Explainer Video
Filmed by our Maths department, this video walks through what ratios and proportional reasoning is from first principles.
Worked Examples
Question 1 - Easy
The table shows the number of daily book sales from three online bookstores over five days. One number is missing from the table.
The number of sales for Store C on Day 4 is missing.
The median number of daily book sales for Store A is .
The ratio of the missing number of daily sales for Store C (with the correct value) to the median for Store A is .
Answer
Worked Solution
Median of Store A
From the sales:
Ratio of Store C’s median to Store A’s
Median of Store C
Question 2 - Medium
The table shows the number of tickets available for five different concerts at a music festival on the first and last day of May, along with the total revenue from ticket sales at the end of the month.
In April of the same year, the total revenue from Concert B ticket sales was £12,800. Assuming the ticket price for Concert B remained the same, what is the ratio of the number of tickets sold for Concert B in April to the number of tickets sold in May?
Answer
Worked Solution
Concert B:
Tickets available on May 1st
Tickets available on May 31st
So, tickets sold in May
Total value on May 31st
So, price per ticket
Tickets Sold in April
Ratio of tickets sold:
April: May
Worked Examples Video