1997 PMWC Problems/Problem I9

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Problem

A chemist mixed an acid of 48% concentration with the same acid of 80% concentration, and then added 2 litres of distilled water to the mixed acid. As a result, he got 10 litres of the acid of 40% concentration. How many millilitre of the acid of 48% concentration that the chemist had used? (1 litre = 1000 millilitres)

Solution

Let the quantity of the 48% acid, in liters, be $x$ . Then the acid of 80% concentration has a volume of $10 - 2 - x = 8 - x$ liters.

$\frac{48}{100}x + \frac{80}{100}(8-x) = \frac{40}{100}(10)$ $\frac{8}{25}x = \frac{12}{5}$ $x = \frac{15}{2}$

There are $1000 \cdot \frac{15}{2} = 7500$ millilitres of the acid.

1997 PMWC (Problems)
Preceded by Problem I8	Followed by Problem I10
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10

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1997 PMWC Problems/Problem I9

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Solution

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