Maths test - to think Civil Service have it wrong?

[Sharingaroomtinightthen]

I’ve just applied for a Civil Service test. Part of it is passing a numerical test.

This is the question.

The answer is 125%. I’m sure of it.

If you start with £100, and in the first year it doubles it’s £200. So at the of year one it’s £200.

In year two it trebles to £600.

It then falls by a quarter in the third year to £450.

So end of year 1 - £200.

End of year 3 - £450.

It’s increased by 125%.

125% isn’t an answer option.

WIBU to email and tell them they’ve got it wrong?

@sandyhappypeople you’re looking at the % multiple not the increase…

125% of 100 = 125

100 increased by 125% of original value is 100+125=225

Seriously, look up the definition of percentage increase, it's not up for interpretation, it's a mathematical formula.

(final value - start value) *100/ start value

So (450-200)*100/200=125

That's it. OP is right.

I’m not wrong. If you increase 200 by 100%, what number do you get?

Increasing something by 100% doubles it though. That's what the question asked - the increase.

What's that got to do with it?

Using the 100 multiplier, as it's easier, you end up with 450, you had 200 end of year 1.

450/200 =........2.25, which is 225% increase.

That Isn’t how you work out percentage increase.

https://www.bbc.co.uk/bitesize/guides/zpjmjty/revision/2

They’re asking for the percentage increase. It’s 125%.

If you increase 100 by 100%, what do you get?

You don't get an increase because because 100% equals 1, it has to be OVER 100% to get an increase or UNDER 100% to get a decrease.

100% is a baseline.

Do it on the calculator if you're not sure, it will give you an answer of 100.

Honestly, the answer to your question is 225%

My mate chatgbt also thinks 125%:

Question Summary

• Year 1: Circulation doubled
• Year 2: Circulation trebled
• Year 3: Circulation fell by 25%
• Question: What is the percentage increase from the end of Year 1 to the end of Year 3?

🔢
Step-by-Step Calculation

1. Assume starting value = 100
2. End of Year 1:
3. 100 × 2 = 200
5. End of Year 2:
6. 200 × 3 = 600
8. End of Year 3:
9. 600 × 0.75 = 450

📈
Calculate Percentage Increase

• From 200 (end of Year 1) to 450 (end of Year 3):
• \frac{450 - 200}{200} \times 100 = \frac{250}{200} \times 100 = 125\%

✅ Actual percentage increase = 125%

❌
Test Each Option Given

• 150% → 200 × 2.5 = 500 ❌
• 225% → 200 × 3.25 = 650 ❌
• 450% → 200 × 5.5 = 1100 ❌
• 550% → 200 × 6.5 = 1300 ❌
• 600% → 200 × 7 = 1400 ❌

✅
Final Answer

• The correct answer is: 125%
• None of the listed options are correct

By the way ChatGPT agrees with you OP

I think the question is open to interpretation because they give an answer that can be worked out (225%) so I can see how the tester thinks that is correct and if they wanted that to be correct then the wording should have been different.

This is what ChatGPT says:

Let's break it down step by step using a starting value of 100 units for easier calculation.
Year 1:
Circulation doubled
→
Year 2:
Circulation trebled (multiplied by 3)
→
Year 3:
Circulation fell by a quarter
→ A fall of 25% means it becomes 75% of the value
→
Now:
We need the percentage increase from the end of the first year (200) to the end of the third year

Percentage Increase = [(450-200)/200] x 100= [(250/200)] x 100 = 125%

Answer: 125% — but wait! That option does not appear in the list.
Let’s read the question again carefully:
"What was the percentage increase in circulation of News Today from the end of the first year to the end of the third?"
Yes — we're measuring from the end of year 1 (200) to the end of year 3 (450).
So the correct percentage increase is 125% — but it's not listed.
The closest answer on the list is 150%, but that is incorrect. This may be a mistake in the options provided.
✅ Correct calculation: 125% increase
❌ No correct option given in the list.

I asked how people might get 225% and it concluded that:
❌ 225% is not mathematically justifiable — it's likely either a mistake by the test writer or a misread of the question.

I then asked about the interpretation I had:
200 increases to 450, if you multiple 200 x 225% you get 450
And asked is it possible that is what tester meant and if so how should have question been worded to get that answer of 225%

Yes — you’ve spotted something really important.

Let’s go through this step by step:

---

✅ You're right:

If you take 200 (the end of year 1 value)

And you multiply it by 225% (i.e., by 2.25)

You get:

200 \times 2.25 = 450

So it's clear: 225% of 200 = 450.

But here’s the key distinction:

> Multiplying by 225% ≠ a 225% increase.

---

🔍 What does multiplying by 225% actually mean?

It means the final value is 225% of the starting value, or 2.25 times the starting value.

That includes the original 100% (the base), so the actual percentage increase is:

225% - 100% = 125% increase

So while 200 × 2.25 = 450 is true, this still represents a 125% increase, not a 225% increase.

---

❗So, if the test writer wanted the answer to be 225%, how should the question have been worded?

Something like:

> "The circulation of News Today at the end of the third year was 225% of what it was at the end of the first year. What is this as a percentage of the end-of-first-year value?"

Or more naturally:

> "By what percentage must the end-of-first-year circulation be multiplied to get the end-of-third-year circulation?"

→ Then the correct answer would be 225% (as a multiplier, not an increase).

---

💡 Summary:

"225% increase" means final = original + 225% of original = 3.25× original

"225% of the original" means final = 2.25× original = 125% increase

---

✅ The original question asked:

> “What was the percentage increase from the end of the first year to the end of the third?”

So the correct answer remains: 125% increase

If they wanted 225% as the correct answer, the question would have needed to ask for a percentage of, not a percentage increase.

I don't think anything I've put here is incorrect.

It's just that percentage increase has a specific meaning - the size of the increase as a % of the original value. So the OP is correct.

Another common way to talk about numbers increasing (or decreasing) is the final value as a percentage of the original value. Which is what the examiner and all the 225% posters are doing. An increase to 225%. But if the examiner wanted that answer they phrased the question badly.

No, it isn’t. It’s 125%.

If you increase 200 by 100%, what number do you get?

So if your electricity bill increases by 50% do you think it halves?

When people get a 4% pay increase do you think they are taking a 96% pay cut? This isn’t how percentage increase works.

But multiplying by 225% is an increase of 125%! Because you started with 100%.

"Multiply by x%" does not equal "increase by x%".

100 x 100% still equals 100, where as 100 increased by 100% (i.e. add 100% to the original 100%) = 200.

Ignoring y1, from end y1 to end y2 it trebles. This means it ends up at 300%. It then reduces from end y2 to end y3 by a quarter a quarter of 300% is 75%. 300% less 75% is 225%.

I wouldn’t contact them to tell them they’re wrong 🤣

That isn’t correct. You’re answering the question, “What percentage of the original number is the new number?”. What they’re actually asking is “What is the percentage increase from the original to the new number?”

To use the example with 100 as a starting point. The end of the first year is 200. The end of the third year is 450.

450 is 225% of 200, you’re right there. But that’s not what they’re asking.

They're asking how much it has increased by. It’s increased by 250 copies. As a percentage, that’s 125% (increase of 200 would be a 100% increase, an increase of 50 would be a 25% increase- add them together).

It is not. If you have a sausage and then you get 100% more sausages you will have two sausages. It’s the increase.

No, your maths is wrong.
If you double a number, you increase it by 100%. If a price rises from £2 to £4 it has gone up by 100%. If it rises from £2 to £4.50 it has gone up 125% (a rise of one and a quarter times the original price).

The correct answer is that the person who wrote the test didn’t word the question properly.
English is my third language, and honestly, I often read questions in emails and think, what the hell do they even want?

No. No. No! You can't add and subtract percentages like that 😲

If something doubles it has increased by 100%.
If it trebles then it has increased by 200%
So the percentage describes the increase (not a multiple of the original amount).

I'm with the op, the right answer is 125%

It's not - it's 225%, no matter how much you don't want it to be.

225% = 2.25 x 200 -> 450

Perhaps try for a different job ?

The question is ambiguous. It's Rachel Reeves arithmetic. Dependent on how you read the question. In the real world you'd have the sales figures then work out the percentages. At he end of the first year sales had doubled to 200. At the end of the second year they trebled to 600. Then they fell by a quarter (150 fewer) to 450. By what percentage is 450 greater than 200? Subtract 200 to get the rise which is 250 then express that as a percentage of 200 = 125%

I’m in awe of your patience!

Youd think with the disaster that is the privatised utilities this sort of nonsense would die out.

No

100% of 200 is 200

200% of 200 is 400

But if you increase 200 by 100%, you get 400

So 400 is 200% OF 200 but 400 is what you get if you increase 200 by 100%