Solution

Step 1 & Step 2: Understanding the Question statement and Drawing Inferences Given info:

• Ratio of alcohol to water in original solution = 7:3

• Let the quantity of original solution be x ml.

⇒ Quantity of alcohol = \(\frac{7\mathrm x}{10}\)

⇒ Quantity of water = \(\frac{3\mathrm x}{10}\)

To find:

• We have to find the quantity of water to be added to the solution, such that the resulting solution contains 60% of alcohol.

• Let the quantity of water that is to be added to the solution be y millilitres.

• So total quantity of final solution will be x+y millilitres

• Now since only water is being added we can infer that the quantity of alcohol in the solution will not change.

• So quantity of alcohol in the final solution will be

• Percentage of alcohol in the final solution should be 60%

⇒ \(\frac{\frac{7\mathrm x}{10}}{(\mathrm x+\mathrm y)}\ast100=60\)

⇒ \(\frac{\frac{7\mathrm x}{10}}{(\mathrm x+\mathrm y)}=\frac35\)

Multiplying both sides of the equation by 5, we get

⇒ \(\frac{\left(\frac{7\mathrm x}{10}\right)\ast5}{(\mathrm x+\mathrm y)}=3\)

⇒ \(\frac{\left(\frac{7\mathrm x}2\right)}{(\mathrm x+\mathrm y)}=3\)

⇒\(3.5x = 3x+3y\)

⇒\(0.5x = 3y\) ...(Equation 1)

• Since we do not know the value of x, we will not be able to determine the value of y.

• So we need a relation in x and y, or value of x or y, to be able to determine the amount of water to be added to the solution.

Step 3: Analyze statement 1 independently• Total quantity of the resulting solution is 350ml.

• Total quantity of the resulting solution = x+y ml (Already established above)

⇒ \(x+y=350ml\) ...(Equation 2)

• Since we have another relation in x and y, we will be able to determine the value of y, and thus the amount of water to be added to the solution.

• Hence statement 1 is sufficient to answer the question.

Step 4: Analyze statement 2 independently• The original solution contains 10.5ml of alcohol for every 4.5ml of water.

• So, \(\frac{\mathrm{Alcohol}}{\mathrm{Water}}=\frac{10.5}{4.5}=\frac73\)

• The ratio of alcohol to water from this statement comes out to be 7:3, which is the same as given to us in the question stem.

• So we do not get any additional information from which we can determine the values of x or y.

• Hence statement 2 is not sufficient to answer the question.

Step 5: Analyze the two statements together• Since from statement 1, we are able to arrive at a unique answer, combining and analysing statements together is not required.

• Hence the correct answer is Option A

Thanks,

Saquib

Quant Expert

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