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      Question

      The question consists of three statements numbered

      “I, II and III” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. A (x + 18) litre mixture contains milk and water, only, in the ratio  5:3 , respectively. Find the value of ‘x’. Statement I:  If 20% of the mixture was replaced with 40 litres of milk, then quantity of milk in the resultant mixture would be 150% more than that of water. Statement II:  If (x – 62) litres of the mixture was replaced with 10 litres of water, then ratio of quantities of milk to that of water in the resultant mixture would be 5:4. Statement III:  If half of the given mixture was mixed with mixture ‘B’ (milk + water) containing 30% water, then quantity of milk would be 48 litres more than that of water in the resultant mixture.
      A The data in statement I alone is sufficient to answer the question, while data in statements II and III alone or together are not sufficient to answer the question. Correct Answer Incorrect Answer
      B The data in statement I and II together are sufficient to answer the question while the data in statement III alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      C The data either in statement I alone or statement III alone are sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      D The data in any of the statements together or alone are not sufficient to answer the question. Correct Answer Incorrect Answer
      E The data in statement II alone is sufficient to answer the question, while the data in statement I alone or statement III alone is not sufficient to answer the question. Correct Answer Incorrect Answer

      Solution

      Statement I: Let the quantity of milk in (x + 18) litre mixture = ‘25y’ litres Then, quantity of water in (x + 18) litre mixture = 25y × (3/5) = ‘15y’ litres After replacing 20% of the mixture with 40 litres of milk, Quantity of milk in the resultant mixture = 25y × (1 – 0.20) + 40 = (20y + 40) litres Quantity of water in the resultant mixture = 15y × (1 – 0.20) = 12y litres According to the statement, (20y + 40) = 12y × 2.5 = 30y So, 10y = 40 So, y = (40/10) = 4 So, (x + 18) = 25y + 15y = 40 × 4 = 160 So, x = 160 – 18 = 142 So, data in statement I alone is sufficient to answer the question. Statement II: After removing (x – 62) litres of mixture, remaining quantity of mixture = (x + 18) – (x – 62) = 18 + 62 = 80 litres Quantity of milk in 80 litres mixture = 80 × (5/8) = 50 litres Quantity of water in 80 litres mixture = 80 – 50 = 30 litres After replacing (x – 62) litres of the mixture with 10 litres of water, Quantity of water in the resultant mixture = 30 + 10 = 40 litres So, ratio of milk to water in the resultant mixture = 50:40 = 5:4 But this information is redundant and with this we cannot determine the value of ‘x’. Therefore, data in statement II alone is not sufficient to answer the question. Statement III: Let the quantity of milk and water in the (x + 18) litres mixture be 10y litres and 6y litres, respectively. Let the total quantity of mixture ‘B’ = 100k litres Then, quantity of water in mixture ‘B’ = 100k × 0.30 = 30k litres So, quantity of milk in mixture ‘B’ = 100k – 30k = 70k litres After mixing half of the (x + 18) litres mixture with mixture ‘B’ Quantity of milk in the resultant mixture = 10y × 0.5 + 70k = (5y + 70k) litres Quantity of water in the resultant mixture = 6y × 0.5 + 30k = (3y + 30k) litres According to the statement, 5y + 70k – 48 = 3y + 30k Or, 2y + 40k = 48 Or, y + 20k = 24 But this equation cannot be solved any further and so, the value of ‘x’ cannot be determined. Therefore, data in statement III alone is not sufficient to solve the question. So, the data in statement I alone is sufficient to answer the question, while data in statements II and III alone or together are not sufficient to answer the question. Hence, option A.

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