# . How many millimetres of water should be added to 9 ml of a shaving lotion containing 50% alcohol to make it a lotion containing 30% alcohol ?

Quantity of alcohol

$= \frac{50}{100} \times 9\\$

Quantity of alcohol = $4.5 \\$ ml

Let the quantity of water to be added = $x \\$ ml

According to the question,

$\frac{4.5}{9 +x}\times 100 = 30 \\ \Rightarrow \frac{4.5}{9 +x} = 0.3 \\ \Rightarrow 4.5 = 2.7 = 0.3x \\ \Rightarrow 0.3x = 1.8 \\ \Rightarrow x = 6\\$

Hence, the quantity of water added $= 6 \\$ ml

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