Question : A mixture of acid and water contains 20% acid. When 10 litres of water is added to the mixture, then the percentage of acid becomes 15%. What is the original quantity of the mixture?
Option 1: 30 litres
Option 2: 25 litres
Option 3: 40 litres
Option 4: 35 litres
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Correct Answer: 30 litres
Solution :
Given: A mixture of acid and water contains 20% acid.
The mixture's ratio = $\frac{(\text{20% acid})}{(\text{80% water})}$ = $\frac{20}{80}$ = 1 : 4.
Let there be $x$ litres of acid in the mixture. Additionally, $4x$ litres of water should be added to the mixture.
According to the question,
$\frac{x}{4x+10}=\frac{15}{85}$
⇒ $\frac{x}{4x+10}=\frac{3}{17}$
⇒ $17x=12x+30$
⇒ $5x=30$
⇒ $x=6$ litres
The mixture's acid content = $x$ = 6 litres.
The mixture's water content = $4x = 4 \times 6$ = 24 litres.
The original mixture's total quantity = 6 + 24 = 30 litres.
Hence, the correct answer is 30 litres.
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