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.
Which is not the function of the Operating System?
Aman bought a goat and a hen, with the goat's cost price being ₹1200 more than the hen's. He sold the hen at a 20% loss and the goat at a 25% profit, ...
10, 11, 7, 34, 18, 125
In the above given series, there is a wrong term. Find the 4th term of another series whose first term is the wrong number...
How many possible values can the digit 'k' take if the number 9458k2 is divisible by 8?
A sum of money becomes ₹7800 after 3 years and ₹8500 after 4 years at simple interest. What is the principal amount?
In a 1500-metre race, Arjun beats Bishnu by 600 metres, and Bishnu beats Chintu by 700 metres. How far will Arjun beat Chintu by ...
(78.03 + 116.98) ÷ 13.211 = 89.9 – 25.23% of ?
A trader buys a stock at an average price of Rs. 240 per share. He sells one-third of his shares at a 10% profit and the remainin...
Anuj invested a certain amount for 18 months at a simple interest rate of 5% per annum and received a total of Rs. 3,440. What wo...
The mean and standard deviation of 6 observations are 10 and 3 respectively. If each observation is multiplied by 4 and then 5 is added to each result, ...
Relevant for Exams:
