Whatever the vendor, a UK numerical reasoning test mostly comes down to six operations: percentages, percentage change, reverse percentages, ratios, weighted averages, and reading more than one table at once. This lesson drills all six, with instant marking, in insurance scenarios, so you pick up the vocabulary while you practise.
Meet Ceredigion Mutual
A motor insurer invented for this course, so every question about it is original:
| Figure | 2024 | 2025 |
|---|---|---|
| (£m) | 84.00 | 90.72 |
| Incurred claims (£m) | 61.00 | 70.00 |
| Expenses (% of premium) | 22% | 22% |
Premium grew 8% between the two years. Note how that figure was built: £84m × 1.08 = £90.72m, a single multiplication by (1 + rate). Working out the 8% separately and adding it on is a second step, and a second chance to fumble under time pressure.
Two definitions
The is claims divided by premium: the share of every premium pound paid back out as claims. The adds the on top. Below 100% the insurer makes an profit, above it a loss.
2024, worked through
Loss ratio: 61 ÷ 84 = 72.6%. Add the 22% and the combined ratio is 94.6%. Underwriting profit is what is left of the premium: 84 - 61 - (0.22 × 84) = £4.52m.
Now do 2025
Work it out
Using the table: what is Ceredigion Mutual's 2025 loss ratio, as a percentage?
Add the 22% and the 2025 combined ratio is 99.2%, 0.8% from break-even. Both years still start with a 9. Premium is up, claims are up. So before reading on, work out what actually happened to the profit.
Work it out
What was Ceredigion Mutual's underwriting profit in 2025, in £m to two decimal places?
That is the point of the example. Both combined ratios < 100%, premium grew 8%, and underwriting profit still fell by 83%, from £4.52m to £0.76m. Growth in the premium hid a collapse in margin (due to increase in combined ratio), and at near 100% combined ratio, moving a few points swings the profit enormously.
Premium is the , profit the : the first and last figures on an income statement. Growth in one tells you nothing about the other, which is what this example is really testing.
Percentage change
The formula is (new - old) ÷ old, and the single most common error under time pressure is dividing by the wrong base. The change is always measured against where you started.
Work it out
By what percentage did Ceredigion Mutual's incurred claims grow from 2024 to 2025, to one decimal place?
Reverse percentages
Test writers use this direction to filter candidates: you are told the figure after growth and asked for the figure before. Divide by (1 + rate). The trap answer comes from subtracting the percentage instead: £90.72m × 0.92 = £83.46m, which looks plausible and is wrong (the true answer is £84m, as you already know).
Work it out
Ceredigion Mutual employs 552 staff in 2025, which is 15% more than in 2023. How many staff did it employ in 2023?
Ratios
A ratio's parts sum to the whole. gives you a natural ratio question: an insurer keeps part of each premium and cedes the rest to a reinsurer.
Work it out
Ceredigion Mutual cedes 2025 motor premium to a reinsurer in the ratio 3:7, ceded to retained. How much of the £90.72m does it retain, in £m?
Weighted averages
The rule: never average the ratios. Total the numerators, total the denominators, then divide once. Ceredigion also writes a small household :
| 2025 | Earned premium (£m) | Incurred claims (£m) |
|---|---|---|
| Motor | 90.72 | 70.00 |
| Household | 29.28 | 16.10 |
Motor runs at 77.2%, household at about 55%. The naive move, averaging those to 66.1%, treats a £29m book as equal to a £91m one, and it is exactly the distractor the answer list will offer.
Work it out
What is Ceredigion Mutual's whole-account loss ratio across motor and household for 2025, as a percentage?
Build it once, instead of eyeballing it six times
Six calculations done on a calculator and forgotten leave you with six answers and nothing you can reuse. The grid below holds the same Ceredigion figures and nothing else. You write every ratio as a formula over the cells, with the in exactly one place, and the sheet then answers the second-order question itself: did underwriting profit rise or fall?
Two notes before you start. You will not have a spreadsheet in the online test itself; that is a calculator and a clock. You will have one in CM1 and CM2 Paper B, both sat in Excel, and on every desk after that. And formulae let you re-run the whole picture on new inputs in seconds, which is how you generate your own drills.
Spreadsheet: build it, don’t type it
The ratio machine
Ceredigion Mutual's motor account sits in A2:C4, with the expense ratio as a single input in B6. The 2025 whole-account split sits in A8:C10. 1. D3 to F4: loss ratio, combined ratio and underwriting result for each year. Write them as decimals, not percentages: 0.726, not 72.6. The underwriting result is premium minus claims minus expenses, in £m, and expenses are the expense ratio times that year's premium. 2. E6: did the underwriting result rise or fall from 2024 to 2025? Use IF to return the word ROSE or the word FELL by comparing the two result cells. 3. B11 and C11: total the two 2025 books. D11: the whole-account loss ratio. AVERAGE is switched off in that cell on purpose: total the numerators, total the denominators, divide once. D4, F4, E6 and D11 are marked. The rest are not marked, but nothing marked comes out right without them. Every ratio must reference B6 rather than carry 0.22 typed into it: change B6 to 0.25 afterwards and watch which cells move.
Cells to fill: D4, F4, E6, D11
- Given data, locked
- Yours to fill
| Row | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| 1 | Ceredigion Mutual - motor account (£m) | |||||||
| 2 | Year | Earned premium | Incurred claims | Loss ratio | Combined ratio | U/W result | ||
| 3 | 2024 | 84 | 61 | |||||
| 4 | 2025 | 90.72 | 70 | |||||
| 5 | ||||||||
| 6 | Expense ratio, both years | 0.22 | Profit rose or fell? | |||||
| 7 | ||||||||
| 8 | 2025 whole account (£m) | Earned premium | Incurred claims | Loss ratio | ||||
| 9 | Motor | 90.72 | 70 | |||||
| 10 | Household | 29.28 | 16.1 | |||||
| 11 | Whole account | |||||||
| 12 | ||||||||
| 13 | ||||||||
| 14 | ||||||||
| 15 |
How this grid works: typing, filling, references, layout
Moving and selecting
- Move a cell at a time
- : arrow keys
- Run to the end of a block
- : Ctrl+arrow
- Back to A1, or out to the last cell used
- : Ctrl+Home / Ctrl+End
- Select a range
- : Shift+arrow, or shift-click the far corner
- Select to the end of a block
- : Ctrl+Shift+arrow
- Take a whole row, or a whole column
- : Shift+Space / Ctrl+Space, or click its header
- Take several rows or columns
- : drag along the headers, or shift-click
- Take the lot
- : Ctrl+A
Entering and editing
- Start an entry
- : just type, or use the formula bar
- Commit it and move down, or up
- : Enter / Shift+Enter
- Commit it and move right
- : Tab
- Change your mind mid-entry
- : Escape
- Open what is already in the cell
- : F2, or double-click it
- Empty the selected cells
- : Delete
- Find a function, then its arguments
- : start typing the name; the open bracket lists the arguments in order, with the one you are writing picked out
Filling and copying
- Fill a formula down the column
- : Ctrl+D, or drag the small square at the corner of the selection
- Fill it right along the row
- : Ctrl+R
- Copy, or cut
- : Ctrl+C / Ctrl+X
- Paste it, references moving as they go
- : Ctrl+V
- Paste the numbers instead of the formulas
- : Ctrl+Shift+V
- Fill a whole block from one cell
- : copy it, select the block, paste
- The same four with a mouse
- : right-click a cell: the shortcuts are printed beside them
References
- Put a cell into a formula without typing its address
- : click it, or press an arrow after =, a bracket or an operator
- Grow that reference into a range
- : Shift+arrow, or drag across the cells
- Stop a reference shifting when the formula copies
- : F4, which adds the dollar signs
- Give the arrow keys back to the text
- : F2 swaps them between picking cells and moving the cursor
- See the range you picked before you commit it
- : each reference takes a colour and outlines the cells it points at; the same one twice keeps its colour
- See what a finished formula reads
- : select its cell: the cells it reads are outlined
Rows and columns
- Make a column wider, or a row taller
- : drag the line between two headers, or Alt+Shift+arrow
- Fit it back to what is in it
- : double-click that line, or Alt+Shift+0
- More room to work in
- : the blank rows and columns past the data, and the Add rows and Add columns buttons
Columns start as wide as what is in them, and nothing you do out in the blank space is marked.
The view
- Zoom in or out
- : Ctrl++ / Ctrl+-, the buttons above the grid, or Ctrl with the wheel
- Back to how it was drawn
- : Ctrl+0, or Reset view
- Find out what a shade means
- : the key above the grid, which lists only the shades this exercise uses
Zoom, widths and heights are how you are looking at the grid, not what is in it. None of it is marked.
Have a go and press Check. The worked solution opens up after your first real attempt.
The closing drill
One last exercise chaining three operations (growth, a ratio, and the combined-ratio assembly) the way a real question set does.
Work it out
Ceredigion Mutual's 2026 plan: motor premium grows a further 6% from £90.72m, claims are expected at £73m, and expenses improve to 21% of premium. What is the planned 2026 combined ratio, as a percentage?