Question

A jar contains a mixture of 175 ml water and 700 ml alcohol. Gopal takes out 10% of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now

• A. 35.2
• B. 30.3
• C. 20.5
• D. 25.4

Answer 1

The Correct Option is A

Step 1: Initial Setup

There are two quantities mixed:

• 700 ml of pure alcohol
• 175 ml of a solution where 90% is alcohol (done twice)

Step 2: Calculate Final Alcohol Quantity

Alcohol contribution from the 90% solution added twice:

\[ \text{Alcohol from second solution} = 175 \times \left(\frac{90}{100}\right)^2 = 175 \times \frac{81}{100} = 141.75 \]

Total alcohol in the mixture:

\[ \text{Final alcohol quantity} = 700 + 141.75 = 841.75 \text{ ml} \]

However, the given answer assumes:

\[ \text{Final alcohol quantity} = \left( \frac{700}{700 + 175} \right) \times \left( \frac{90}{100} \right)^2 \times (700 + 175) = \frac{700}{875} \times \frac{81}{100} \times 875 = 567 \text{ ml} \]

Step 3: Compute Water Quantity

Total volume of mixture = \( 700 + 175 = 875 \) ml

\[ \text{Water quantity} = 875 - 567 = 308 \text{ ml} \]

Step 4: Find Percentage of Water

\[ \text{Percentage of water} = \left( \frac{308}{875} \right) \times 100 = \boxed{35.2\%} \]