Multiple choice

Directions: The question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and mark the correct answer. Jar A comprises a mixture of milk and water in the ratio of 3 : 2, respectively. Another mixture of milk and water is added to Jar A and the ratio of milk and water in the resultant mixture changes. What is the initial quantity of mixture present in Jar A? I. The ratio of milk and water in the mixture that is added to Jar A is 2 : 1, respectively. II. The ratio of the new quantities of milk and water in Jar A is 8 : 5, respectively. The quantity of water in the mixture added to Jar A was 6 litres.

  1. The data in both the statements I and II together is necessary to answer the question.

  2. The data in either statement I alone or statement II alone is sufficient to answer the question.

  3. The data in both the statements I and II together is not sufficient to answer the question.

  4. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  5. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
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A Correct answer
Explanation

To find the initial quantity, we need the initial ratio (given as 3:2), the ratio of the added mixture (given in I), the final ratio (given in II), and the absolute quantity of one component added (given as 6 liters of water). All these pieces of information are required to set up and solve the system of equations.

AI explanation

Using the rule of alligation on the ratios of milk to total mixture (3/5 for Jar A and 2/3 for the added mixture) versus the final ratio (8/13), the ratio of initial volume to added volume is 1:1. Statement II provides the quantity of water added, meaning 6 litres is one-third of the total added mixture, making the total added mixture 18 litres. Since the initial and added volumes are equal, both statements are required to determine the initial quantity is 18 litres.

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