Question
A mixture contains 75% alcohol and rest water. A man
withdrew some mixture using a cup and replaced it with same quantity of petrol, such that the quantity of alcohol remaining in the mixture now is 60%. If the man wants to bring down the quantity of alcohol to less than 40%, then how many more times should he repeat the same process?Solution
Let the percentage of mixture withdrawn first time be ‘p%’. ATQ; 75 × {1 − (p/100)} = 60 Or, 1 − (p/100) = 0.8 Or, (p/100) = 0.2 So, p = 20 So, 20% mixture is drawn every time. Now, Quantity of alcohol remaining after withdrawing once more = 60 × 0.8 = 48 And,
Quantity of alcohol remaining after withdrawing once more = 48 × 0.8 = 38.4 So, after withdrawing two more times, the quantity of alcohol reaches less than 40%.
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