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Each question given consists of question and two statements numbered I and II given you have to decide whether data provided in statement sufficient to answer question read both statement and give answer
What was initial quantity of juice in mixture of juice and water
I.initial quantity of mixture was 25 litres
II.initial quantity of juice in mixture was 70% after adding 10 l of water it became 50%

A

if the data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question

B

if the data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question

C

if the data in statement I alone or in statement II alone are sufficient to answer the question

D

if the data in both statement I alone or in statement II alone are not sufficient to answer the question

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the initial quantity of juice in a mixture of juice and water based on the information provided in the two statements. ### Step-by-Step Solution: 1. **Analyze Statement I**: - Statement I states that the initial quantity of the mixture was 25 liters. - This means the total volume of juice and water combined is 25 liters. - However, this statement does not provide any information about the proportion of juice to water. Therefore, we cannot determine how much of that 25 liters is juice. - **Conclusion**: Statement I alone is not sufficient to answer the question. 2. **Analyze Statement II**: - Statement II states that the initial quantity of juice in the mixture was 70%. After adding 10 liters of water, the juice became 50% of the mixture. - Let the initial quantity of the mixture be \( x \) liters. - According to the statement, the initial quantity of juice is \( 0.7x \) liters (70% of \( x \)) and the initial quantity of water is \( 0.3x \) liters (30% of \( x \)). - After adding 10 liters of water, the new quantity of water becomes \( 0.3x + 10 \) liters. - The total quantity of the mixture after adding water is \( x + 10 \) liters. - The new percentage of juice in the mixture is given as 50%, which can be expressed as: \[ \frac{0.7x}{x + 10} = 0.5 \] - To solve for \( x \), we can cross-multiply: \[ 0.7x = 0.5(x + 10) \] - Expanding the right side: \[ 0.7x = 0.5x + 5 \] - Rearranging gives: \[ 0.7x - 0.5x = 5 \] \[ 0.2x = 5 \] - Solving for \( x \): \[ x = \frac{5}{0.2} = 25 \text{ liters} \] - Now, we can find the initial quantity of juice: \[ \text{Initial quantity of juice} = 0.7x = 0.7 \times 25 = 17.5 \text{ liters} \] - **Conclusion**: Statement II alone is sufficient to answer the question. 3. **Final Conclusion**: - Statement I alone is not sufficient. - Statement II alone is sufficient. - Therefore, the answer is that data in statement II alone are sufficient to answer the question, while data in statement I alone are not sufficient.
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