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In a 84 litres mixture the alcohol and water are in the ratio of 3 : 4 respectively. 14 litres of mixture is taken off and replaced with 20 litres of water. What is the new ratio of alcohol and water respectively?

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DFCCIL Executive CBT1 Civil 25 Aug 2023 Shift 3 Official Paper
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  1. 2 : 1
  2. 1 : 2
  3. 3 : 1
  4. 1 : 1

Answer (Detailed Solution Below)

Option 2 : 1 : 2
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Detailed Solution

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Given:

Total volume of mixture = 84 liters

Ratio of alcohol to water = 3:4

Volume of mixture taken off = 14 liters

Volume of water added = 20 liters

Formula Used:

New ratio = (Remaining alcohol) : (Remaining water + added water)

Calculation:

Initial volume of alcohol = (3/7) × 84 = 36 liters

Initial volume of water = (4/7) × 84 = 48 liters

Volume of alcohol taken off = (3/7) × 14 = 6 liters

Volume of water taken off = (4/7) × 14 = 8 liters

Remaining alcohol = 36 - 6 = 30 liters

Remaining water = 48 - 8 = 40 liters

New volume of water = 40 + 20 = 60 liters

New ratio of alcohol to water = 30:60

Simplifying the ratio: 30:60 = 1:2

The new ratio of alcohol and water is 1:2.

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