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
- 35.2
- 30.3
- 20.5
- 25.4
The Correct Option is A
Solution and Explanation
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
\[ \text{Percentage of water} = \left( \frac{308}{875} \right) \times 100 = \boxed{35.2\%} \]
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