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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