Question
The question consists of two statements numbered "I and
II" given below it. You have to decide whether the data provided in the statements are suicient to answer the question. A mixture consists of 25 litres of water and 'n' litres of honey. Determine the total volume of the mixture. Statement I: After adding (n - 50) litres of water to the mixture, the ratio of honey to water becomes 3:2. Statement II: After removing 20 litres from the mixture, the amount of honey left is 60 litres.Solution
ATQ,
Total volume of the mixture = (n + 25) litres Statement I: (25 + n - 50) : n = 2 : 3 => 3 × (n - 25) = 2n => 3n - 75 = 2n => n = 75 Total volume of the mixture = 75 + 25 = 100 litres Hence, Statement I alone provides enough data to answer the question. Statement II: Initial ratio of milk to the total mixture = n / (n + 25) After removing 20 litres of mixture: Remaining volume = n + 5 litres Remaining quantity of milk = 60 litres New milk ratio = 60 / (n + 5) So, n / (n + 25) = 60 / (n + 5) ⇒ 60n + 1500 = n² + 5n ⇒ n² - 55n - 1500 = 0 ⇒ n² + 20n - 75n - 1500 = 0 ⇒ n(n + 20) - 75(n + 20) = 0 ⇒ (n - 75)(n + 20) = 0 So, n = 75 (since n cannot be negative) Total volume = 75 + 25 = 100 litres Thus, Statement II alone is also sufficient. Final Conclusion: Either Statement I alone or Statement II alone is sufficient to determine the total quantity of the mixture.
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