ESAT Maths 1 · free worked solution

ESAT Maths 1 dilution: find the original volume

Dilution solution: set up the unchanged acid amount and solve for the original 32-litre volume.

Dilution and concentrationSpecification M3.5Reviewed 5 August 2026

Answer first

Option C

The correct answer is

$32 \text{ litres}$

Adding water changes the total volume, but it does not change the amount of acid already present.

This is original UniGenius practice material from the reviewed Maths 1 bank. It is not an official UAT-UK question, past paper, or recalled question.

The question

Read the setup, then choose the shortest valid route

A container holds a solution that is $35\%$ acid by volume. After $8 \text{ litres}$ of water are added, the solution is $28\%$ acid. What was the original volume of the solution?

A $64 \text{ litres}$
B $48 \text{ litres}$
C $32 \text{ litres}$ Answer
D $35 \text{ litres}$
E $40 \text{ litres}$

Worked solution

The route in 4 steps

Let the original volume be V litres, so the volume of acid is $0.35\text{V}$ litres.
Adding 8 litres of water changes the total volume to $\text{V} + 8$ but does not change the acid volume.
The new concentration gives $0.35\text{V} = 0.28(\text{V} + 8)$ .
Thus $0.07\text{V} = 2.24$ , so $\text{V} = 32 \text{ litres}$ .

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