EPSO-Style Numerical Reasoning — Ratios (Advanced)
Instructions
You will be presented with 10 ratio & proportion questions.
Your task is to analyse the information carefully and select the correct answer.
- Only one answer option is correct per question.
- You have 20 minutes to complete all 10 questions.
- You may use the onscreen calculator and the scratchpad for note-taking.
When ready, proceed using the button below.
Pro Tip — Ratios in 10 seconds
Always convert a ratio to total parts first. Then either:
- Find one part (Total ÷ parts), or
- Turn it into a fraction (e.g. 3:5 → 3/8 and 5/8).
Most wrong answers come from using the wrong denominator (end value instead of start / wrong “whole”).
Quiz Summary
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Question 1 of 10
1. Question
DG Staffing Transition
A DG has staff on contract and permanent posts in the ratio 5:3.
After recruiting 32 permanent staff (contracts unchanged), the ratio becomes 5:4.
Question: How many staff did the DG have initially?
Calculator:
CorrectIncorrectHint
- Represent the two groups as 5k and 3k.
- Add 32 only to permanent staff.
- Use the new ratio to build one equation.
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Question 2 of 10
2. Question
EU Programme Envelope Reallocation
A total of €2.4 billion is split across Programmes A, B and C in the ratio 4:7:9.
Then €120 million is reallocated from Programme C to Programme A.
Question: What is the new ratio A : B : C?
Calculator:
CorrectIncorrectHint
- Find the value of 1 ratio part first.
- Apply €120m from C to A (B unchanged).
- Turn the new amounts back into a simplified ratio.
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Question 3 of 10
3. Question
Humanitarian Stockpile Adjustment
An EU stockpile contains medical kits and tents in the ratio 11:4.
After adding 35 tents (kits unchanged), the ratio becomes 11:5.
Question: How many tents were in the stockpile before the delivery?
Calculator:
CorrectIncorrectHint
- Use variables: kits=11k, tents=4k.
- Only tents change (+35).
- Use the new ratio 11:5 to solve for k.
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Question 4 of 10
4. Question
Member State Co-Financing
Three Member States contribute to a joint action in the ratio 5:4:3 (DE:FR:IT), totalling €1.44 billion.
Italy increases its contribution by €120 million (others unchanged).
Question: What percentage of the new total does Italy contribute?
Calculator:
CorrectIncorrectHint
- Convert €1.44bn to €1,440m.
- Use ratio parts to find Italy’s initial amount.
- After +€120m, divide Italy by the new total.
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Question 5 of 10
5. Question
Erasmus+ Redistribution
Participants are initially allocated to Destinations A, B and C in the ratio 2:3:5.
Then 60 participants are moved from C to A (B unchanged).
After the move, the number in A equals the number in B.
Question: How many participants were allocated in total initially?
Calculator:
CorrectIncorrectHint
- Write A,B,C as 2k,3k,5k.
- Move 60 from C to A (total unchanged).
- Set A=B and solve k, then total=10k.
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Question 6 of 10
6. Question
IT Procurement: Devices Difference
A service purchases laptops and tablets in the ratio 4:1.
The number of laptops is 180 more than the number of tablets.
Question: How many devices were purchased in total?
Calculator:
CorrectIncorrectHint
- Translate into parts: laptops=4k, tablets=1k.
- Use the difference: 3k = 180.
- Total is 5k once k is known.
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Question 7 of 10
7. Question
Humanitarian Envelope: Flexibility Increase
An envelope is split between core funding and flexible reserve in the ratio 9:1.
After adding €50 million to the flexible reserve (core unchanged), the ratio becomes 3:1.
Question: What was the initial total envelope (in € million)?
Calculator:
CorrectIncorrectHint
- Set core=9k and flex=k.
- Only flex changes: k+50.
- Use new ratio 3:1 to solve k; total=10k.
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Question 8 of 10
8. Question
DG Unit Reassignment
In a unit, the ratio of policy officers to support staff is 5:7.
After reassigning 24 support staff to policy roles (total unchanged), the two groups become equal in size.
Question: How many staff are in the unit?
Calculator:
CorrectIncorrectHint
- Represent groups as 5k and 7k.
- Transfer affects both sides (+24 and −24).
- Set the new values equal and solve for k.
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Question 9 of 10
9. Question
Working Time Conversion
The ratio of part-time to full-time staff is 3:5.
After converting 20 part-time staff to full-time, the ratio becomes 1:2.
Question: How many full-time staff were there initially?
Calculator:
CorrectIncorrectHint
- Represent groups as 3k and 5k.
- Apply the conversion: part-time decreases, full-time increases.
- Use the new ratio 1:2 to solve for k.
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Question 10 of 10
10. Question
Administrative vs Operational Budget
A budget is split between administrative and operational costs in the ratio 2:7.
Operational costs are €1.05 billion.
Question: What is the—all-in—total budget (in € billion)?
Calculator:
CorrectIncorrectHint
- Operational corresponds to 7 parts.
- Find 1 part by dividing 1.05 by 7.
- Multiply 1 part by total parts (9).
