ReasoningCampus · Online SHL preparation
Chart Units and Ratios: Our SHL Method and 6 Practice Questions
A numerical reasoning question may need only one division, yet the hard part is deciding which two numbers belong in it. ReasoningCampus offers SHL numerical preparation that starts with reading the chart: its units, time period, categories and requested comparison. This lesson focuses on that translation from displayed data to a defensible calculation.
Numerical reasoning means using quantities to answer a question, not carrying out arithmetic in isolation. A chart can mix thousands of euros, thousands of orders, percentages and cumulative totals. We will slow down the reading step, practise ratios and conversions, and show how a quick estimate can catch an answer that is numerically tidy but answers the wrong question.
View full preparationSHL numerical reasoning question types: a practical study map
SHL’s public interactive numerical reasoning fact sheet describes decisions based on numerical information and activities involving charts, graphs and spreadsheets. Numerical calculation is a separate product family. The study map below covers useful mathematical relationships for preparation; it is not an exhaustive disclosure of SHL’s item bank, nor a guarantee of your assessment mix.
| Relationship | Typical calculation | Where to focus |
|---|---|---|
| Differences and comparisons | A − B; identify largest or smallest. | Compare the same period and unit. |
| Percentage change and reverse percentages | (New − old) ÷ old; original = final ÷ multiplier. | Use the original base. See the reverse-percentage lesson. |
| Shares, ratios and allocations | Part ÷ whole; A share = total × a/(a+b). | A:B is not A divided by the whole. |
| Averages and combined rates | Total contribution ÷ total observations or other relevant base. | Use the weighted-averages lesson for unequal groups. |
| Rates and unit conversions | Quantity ÷ time; convert units before combining. | State assumptions before projecting a rate. |
| Revenue, cost, profit and margin | Profit = revenue − cost; margin = profit ÷ revenue. | Markup on cost has a different denominator. |
| Cumulative and period totals | Current cumulative − previous cumulative. | A running total is not that month’s value. |
| Overlapping groups | A or B = A + B − both. | Subtract the overlap once. |
For a bar chart, read the axis scale before comparing heights. For a pie chart, identify the total that the shares refer to. For a line graph, check the period and whether the values are cumulative. A table may hide the scale in a heading rather than beside each number. Those reading habits apply before any formula.
One small example: margin is not markup
If revenue is £250 and cost is £200, profit is £50. Profit margin is £50 ÷ £250 × 100 = 20%; markup on cost is £50 ÷ £200 × 100 = 25%. Both calculations are correct, but they answer different questions. Underline the requested denominator before using the figures. The questions below develop the same habit with chart scales, exchange rates and group totals.
Chart units: the ReasoningCampus quantity-and-unit check
Write four labels next to the values you select: quantity, unit, period and population. Then state the requested result in words, such as revenue per order. Cancel or convert units in the working before evaluating the number. A numerically tidy result can still be wrong if it compares different periods or counts the same category twice.
Before calculating, write four short labels: quantity, unit, period and population. A revenue figure in thousands of euros for one quarter cannot be compared directly with a monthly value in euros. Nor can the number of orders be used as the number of customers unless the task says they are the same.
| Check | Example | Risk if ignored |
|---|---|---|
| Quantity | Revenue, orders, customers or hours? | Dividing by the wrong denominator. |
| Unit | Euros, €000, units or thousands of units? | A factor-of-1,000 error. |
| Period | One month, one quarter or one year? | Comparing unlike durations. |
| Population | All orders or only completed orders? | Combining incompatible groups. |
Keep units in the working
If revenue is €240,000 and orders are 6,000, revenue per order is €240,000 ÷ 6,000 orders = €40 per order. If the table displays 240 in a column labelled “€000” and 6 in a column labelled “orders, thousands”, both scale factors cancel. If the orders column instead displays 6,000 actual orders, only the revenue needs scaling.
Distinguish a ratio from a percentage share
If team sizes are in the ratio 3:5, there are eight ratio parts altogether. The first team is 3 ÷ 8 = 37.5% of the total, not 3 ÷ 5 = 60%. The latter compares the first team with the second team. Both calculations can be meaningful, but they answer different questions.
Check the graph as well as the numbers
- Read whether an axis starts at zero or is truncated; visual bar height alone may mislead.
- Check whether values are totals, cumulative values or changes during the period.
- Use the exact labels when supplied. If a chart gives only approximate values, do not claim unsupported decimal precision.
- Check whether categories overlap before summing them.
- Round at the requested final stage, after the relevant conversions.
SHL describes its numerical practice as involving tables of numerical data. The charts and examples here are our own teaching material. Your invitation determines the actual format, tools and time allowed.
Data interpretation: check the comparison before calculating
For revenue of £240,000 and 12,000 orders, record “£240,000 ÷ 12,000 orders = £20 per order”. If a table reports both quantities in thousands, the two scale factors cancel. If only one quantity is in thousands, they do not. This is why we teach you to retain unit labels until the last step.
Worked numerical examples: scale, ratio and time period
Example 1: same total, different revenue per order
| Branch | Revenue (€000) | Completed orders (thousands) |
|---|---|---|
| North | 360 | 12 |
| South | 270 | 6 |
North: €360,000 ÷ 12,000 = €30 per completed order. South: €270,000 ÷ 6,000 = €45 per completed order. North has higher total revenue but lower revenue per completed order. Read which comparison the question asks for.
Example 2: divide a total in a ratio
Allocate 640 training places between two regions in a 3:5 ratio. Total parts = 8; one part = 640 ÷ 8 = 80. Allocations are 3 × 80 = 240 and 5 × 80 = 400. Check: 240 + 400 = 640 and 240:400 simplifies to 3:5.
If the total does not divide into whole places, the question must provide or imply an allocation convention. Do not silently round both groups independently and change the total.
Example 3: convert a quoted exchange rate in the right direction
At a stated rate of €1 = $1.20, $720 corresponds to €600: $720 ÷ ($1.20 per euro). Check by converting back: €600 × 1.20 = $720. This is a fictional rate for the exercise, not a current market rate.
Example 4: observed average versus forecast
A department handles 900 cases over three months. Its average over those months is 300 cases per month. Multiplying by 12 gives 3,600 as an annualised figure if the same average is assumed to continue. The three-month observation alone does not establish the actual annual total.
A five-second sense check
Ask whether the answer has the right dimension and order of magnitude. A result of €0.03 per order for the North branch should prompt a unit check. A first allocation larger than the second is inconsistent with a 3:5 ratio. A forecast should not be reported as an observed result.
Next, study weighted averages when group sizes differ and reverse percentages when the original base is unknown. Those lessons address different denominator problems.
Try the revenue-per-order unit calculator
Enter values exactly as displayed in a fictional table, then choose the scale of each column. The tool converts both to base units before division. It assumes the figures refer to the same period and the same set of orders; you must check that context yourself.
Static check: revenue 360 in €000 and orders 12 in thousands gives €30 per order. Revenue 360 in €000 and orders 12 in actual orders gives €30,000 per order. Changing a column label changes the meaning even when the displayed number is unchanged.
Chart units: six explained practice questions
Try all six questions before opening the worked answers below. Submit your choices to see your score and individual feedback. You can change your choices before submission, or go straight to the answers and explanations for self-study.
This is an original ReasoningCampus learning check. One point is awarded per correct answer. The total is not an SHL score, a percentile, a pass prediction or a personality profile.
Answers and complete worked explanations
Open any question below to study the correct answer, the alternatives, the method and the common trap. These explanations are available without completing the quiz.
Review the reasoning in any missed or uncertain answer. The score describes this small set only.
Question 1: Two scale factors cancel
Correct answer: B. €30
Write the units alongside the values: revenue is €450,000 and orders are 15,000. Revenue per order is €450,000 ÷ 15,000 = €30, so B is correct. Because both table entries use thousands, the scale factors cancel: (450 × 1,000) ÷ (15 × 1,000) = 450 ÷ 15.
A introduces an extra division by 1,000. D converts the revenue to euros but leaves the order count at 15, making the result 1,000 times too large. C also gives an incompatible scale; €3,000 × 15,000 orders would imply €45 million, not €450,000. Multiplying the proposed average back by the number of orders is a quick way to expose a unit error.
Question 2: Split the total
Correct answer: C. €360
The ratio 3:5 divides the whole into eight equal parts, not five. Each part is 960 ÷ 8 = 120. Group A receives three parts, so A’s share is 3 × 120 = 360, option C. Group B receives five parts, 600, and the two amounts add back to 960.
A uses 3/5 of the total, confusing the ratio of A to B with the fraction of A in the whole. B gives B’s share rather than A’s. D divides by three without first identifying the total number of parts. Write “A:B” above the ratio and “A/(A+B)” beside the required fraction; that small label prevents a common denominator mistake.
Question 3: Exchange-rate direction
Correct answer: D. €600
Use the exchange-rate statement as an equation: euros × 1.20 dollars per euro = dollars. To recover euros from $720, reverse that multiplication: 720 ÷ 1.20 = €600. D is correct. Check it forwards: €600 × $1.20/€ = $720.
A multiplies by 1.20 again, which is the wrong conversion direction. B ignores the exchange rate. C reduces the dollar amount by an unsupported percentage. You do not need a memorised rule such as “always multiply when converting currency”; the direction depends on how the rate is quoted. Keeping the currency units in the calculation tells you which operation cancels dollars and leaves euros.
Question 4: Cumulative data
Correct answer: A. 75
A cumulative figure includes the earlier periods. The March total of 195 therefore contains February’s cumulative 120 plus the amount added during March. Subtract: 195 − 120 = 75, so A is correct. The relationship is March-only = cumulative-to-March − cumulative-to-February.
B reports the running total instead of the month’s contribution. C adds the cumulative figures and counts the earlier amount twice. D repeats the February figure. Before doing any arithmetic with a time-series table, look for words such as “cumulative”, “year to date” or “to date”. They change what each displayed number represents even when the column headings are simply month names.
Question 5: Average is not a guarantee
Correct answer: B. Its average over the observed period was 300 per month
The data support an average: 900 cases ÷ 3 months = 300 cases per month, B. An average summarises the total across the period; it does not reveal how the total was distributed or guarantee what happens next. For example, 200, 300 and 400 cases would produce the same three-month average.
A projects the average over a full year without evidence that the pace will continue. C claims every observed month had exactly 300 cases, which the total alone does not establish. D predicts the next month. Those claims may be reasonable planning assumptions in another task, but they are not deductions from the figures supplied here.
Question 6: Overlapping categories
Correct answer: C. 90
Adding 60 people in A and 50 in B counts the 20 people in both groups twice. Subtract that overlap once: 60 + 50 − 20 = 90, C. You can verify it by separating the population into A only = 40, B only = 30, both = 20, and neither = 10. The first three groups total 90 and all four total 100.
A leaves the double count in place. B subtracts the overlap twice, removing people who should remain in the union. D does not match the stated group counts. The word “either” can be ambiguous in everyday speech, so use the question’s explicit meaning here: at least one of the two groups includes those who belong to both.
SHL numerical preparation at ReasoningCampus: data interpretation
Our online SHL preparation includes numerical data interpretation and worked calculations. This lesson teaches the checks that come before the arithmetic. Combine it with the weighted-averages or reverse-percentages lesson when a question requires both reading the data and choosing a calculation.
Choose your next practice step
- Your answer is too large or too small by a factor of 1,000. Rewrite both quantities with their full units and inspect the conversion.
- You divided an overall total into a ratio incorrectly. Calculate the total number of parts, then find one part before allocating the amounts.
- You treated an observed average as a guaranteed future value. Return to the time-period example and separate what is reported from what is forecast.
Explore the ReasoningCampus SHL preparation materials and choose the areas named in your assessment invitation.
Chart units: practical FAQs
Can I cancel “thousands” before dividing?
Yes, when both numerator and denominator carry the same factor and refer to the required quantities. If only one column is in thousands, canceling both would be wrong.
Why is 3:5 not a 60% share of the total?
Three fifths compares the first group with the second. The first group’s share of their combined total is 3 divided by 8, or 37.5%.
Should I estimate from a chart or calculate exactly?
Use supplied exact labels where available and follow the question’s requested precision. If the display only supports an approximation, do not invent extra precision.
Can I multiply a quarterly total by four?
That produces an annualised amount under an assumption that the same quarterly level continues. It does not establish the actual annual total unless the question supplies the necessary condition or data.
Does the calculator check that my populations match?
No. It handles the unit conversion and arithmetic only. You must verify that revenue and orders cover the same period, location and inclusion criteria.
What should I study after units and ratios?
Use weighted averages for groups of unequal size and reverse percentages when recovering an original amount. ReasoningCampus teaches these in separate lessons with worked practice, linked above.
Official sources and how this lesson was prepared
The SHL references below provide the assessment context. The teaching method, fictional examples, diagrams, tools and explained practice answers are ReasoningCampus learning material; they are not official SHL questions or scoring rules.
AI assistance was used in research, drafting and implementation. Calculations, logic and the page tools were checked during preparation. These lessons are independent educational material; the methods are not SHL scoring rules. Read about ReasoningCampus or send a correction or question.
Additional official format references: SHL interactive numerical reasoning fact sheet and SHL interactive numerical calculation fact sheet. Read the specification for the product actually named in your invitation.
