The question below is followed by two statements I and II. You have to

1.	The question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question.A certain liter mixture contains milk and water in the ratio 7 : 5 respectively. The milkman sold 36 liters of the mixture. Find the quantity of milk in the initial mixture.Statement I: If sham adds 15 liters of pure milk and 5 liters of water to the remaining mixture, ratio of milk and water in the final mixture becomes 5 : 3 respectively.Statement II: If sham sold 24 liters of the remaining mixture and adds 3 liters of water to the remaining mixture, ratio of milk and water in the final mixture becomes 7 : 6 respectively. 1. if the statement I alone is sufficient to answer the question, but the statement II alone is not sufficient.2. if the statement II alone is sufficient to answer the question, but the statement I alone is not sufficient.3. if either the statement I alone or statement II alone is sufficient to answer the question.4. if you cannot get the answer from the statement I and II together, but need even more data.5. None of the above
Answer» Correct Answer - Option 3 : if either the statement I alone or statement II alone is sufficient to answer the question. Let, initial quantity of mixture be y liters. Quantity of milk in the initial mixture = 7y/12 Quantity of water in the initial mixture = 5y/12 Quantity of milk in the remaining mixture = 7y/12 – 7/12 × 36 = 7y/12 – 21 Quantity of water on the remaining mixture = 5y/12 – 5/12 × 36 = 5y/12 – 15 From I: (7y/12 – 21 + 15)/(5y/12 – 15 + 5) = 5/3 ⇒ (7y/12 – 6)/(5y/12 – 10) = 5/3 ⇒ 3 × (7y/12 – 6) = 5 × (5y/12 – 10) ⇒ 7y/4 – 18 = 25y/12 – 50 ⇒ 25y/12 – 7y/4 = 50- 18 ⇒ (25y – 21y)/12 = 32 ⇒ 4y/12 = 32 ⇒ y/3 = 32 ⇒ y = 96 liters Quantity of milk in the initial mixture = 7/12 × 96 = 56 liters. From II: (7y/12 – 21 – 7/12 × 24)/(5y/12 – 15 – 5/12 × 24 + 3) = 7/6 ⇒ (7y/12 – 21 – 14)/(5y/12 – 15 10 + 3) = 7/6 ⇒ (7y/12 – 35)/(5y/12 – 22) = 7/6 ⇒ 6 × (7y/12 – 35) = 7 × (5y/12 – 22) ⇒ 42y/12 – 210 = 35y/12 – 154 ⇒ 7y/12 = 56 ⇒ y = 56 × 12/7 ⇒ y = 96 liters Quantity of milk in the initial mixture = 7/12 × 96 = 56 liters. Hence, either the statement I alone or statement II alone is sufficient to answer the question.

The question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question.A certain liter mixture contains milk and water in the ratio 7 : 5 respectively. The milkman sold 36 liters of the mixture. Find the quantity of milk in the initial mixture.Statement I: If sham adds 15 liters of pure milk and 5 liters of water to the remaining mixture, ratio of milk and water in the final mixture becomes 5 : 3 respectively.Statement II: If sham sold 24 liters of the remaining mixture and adds 3 liters of water to the remaining mixture, ratio of milk and water in the final mixture becomes 7 : 6 respectively. 1. if the statement I alone is sufficient to answer the question, but the statement II alone is not sufficient.2. if the statement II alone is sufficient to answer the question, but the statement I alone is not sufficient.3. if either the statement I alone or statement II alone is sufficient to answer the question.4. if you cannot get the answer from the statement I and II together, but need even more data.5. None of the above

Answer» Correct Answer - Option 3 : if either the statement I alone or statement II alone is sufficient to answer the question.

Let, initial quantity of mixture be y liters.

Quantity of milk in the initial mixture = 7y/12

Quantity of water in the initial mixture = 5y/12

Quantity of milk in the remaining mixture = 7y/12 – 7/12 × 36 = 7y/12 – 21

Quantity of water on the remaining mixture = 5y/12 – 5/12 × 36 = 5y/12 – 15

From I:

(7y/12 – 21 + 15)/(5y/12 – 15 + 5) = 5/3

⇒ (7y/12 – 6)/(5y/12 – 10) = 5/3

⇒ 3 × (7y/12 – 6) = 5 × (5y/12 – 10)

⇒ 7y/4 – 18 = 25y/12 – 50

⇒ 25y/12 – 7y/4 = 50- 18

⇒ (25y – 21y)/12 = 32

⇒ 4y/12 = 32

⇒ y/3 = 32

⇒ y = 96 liters

Quantity of milk in the initial mixture = 7/12 × 96 = 56 liters.

From II:

(7y/12 – 21 – 7/12 × 24)/(5y/12 – 15 – 5/12 × 24 + 3) = 7/6

⇒ (7y/12 – 21 – 14)/(5y/12 – 15 10 + 3) = 7/6

⇒ (7y/12 – 35)/(5y/12 – 22) = 7/6

⇒ 6 × (7y/12 – 35) = 7 × (5y/12 – 22)

⇒ 42y/12 – 210 = 35y/12 – 154

⇒ 7y/12 = 56

⇒ y = 56 × 12/7

⇒ y = 96 liters

Quantity of milk in the initial mixture = 7/12 × 96 = 56 liters.

Hence, either the statement I alone or statement II alone is sufficient to answer the question.

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