Question
Download Solution PDFThe alcohol and water in a mixture are in the ratio of 7 : 8 respectively. If 11 litre water is added to it, then the ratio of alcohol and water in the new mixture becomes 3 : 5. What is the total quantity (in litres) of the alcohol in the new mixture?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The alcohol and water in a mixture are in the ratio of 7 : 8 respectively. If 11 litre water is added to it, then the ratio of alcohol and water in the new mixture becomes 3 : 5.
Calculation:
Suppose total mixture = 15x liters
Alcohol content = 7/15 × 15x = 7x liters
Water content = 15 - 7 = 8x liters
According to the question,
7x/(8x + 11) = 3/5
⇒ 35x = 24x + 33
⇒ 33 = 11x
⇒ x = 3
∴ Alcohol content in final mixture 7 × 3 = 21 liters
Shortcut Trick
The alcohol and water are in the ratio of 7 : 8
Now, 11 litre water is added and ratio becomes 3 : 5
So, we have to equal the unit of alcohol in both the ratio
So, water is added (35 - 24) = 11 unit → 11 litr
So, quantity of alcohol is 21 unit → 11/11 × 21 = 21 liters
Last updated on May 28, 2025
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