Question : In a mixture, the ratio of a chemical X and water is 15 : 9. When 48 litres of this mixture is replaced with water, the ratio becomes 11 : 13. Find the quantity of water after replacement.
Option 1: 97.5 litres
Option 2: 99 litres
Option 3: 92 litres
Option 4: 102.5 litres
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Correct Answer: 97.5 litres
Solution : The ratio of a chemical X and water = 15 : 9 = 5 : 3 Let the quantity of chemical X be 5x and the quantity of water be 3x. Quantity of mixture replaced by water = 48 litres According to the question, (5x – 48($\frac{5}{8}$) : (3x – 48($\frac{3}{8})$ + 48) = 11 : 13 ⇒ (5x – 30) : (3x + 30) = 11 : 13 ⇒ 13(5x – 30) = 11(3x + 30) ⇒ 65x – 390 = 33x + 330 ⇒ 32x = 720 ⇒ x = 22.5 So, water after replacement = 3 × (22.5) – 48 × ($\frac{3}{8}$) + 48 = 97.5 litres Hence, the correct answer is 97.5 litres.
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