# A container contains a mixture of water and alcohol in the ratio 7 : 5. When 18 liters of mixture are drawn off and the container is filled with alco

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A container contains a mixture of water and alcohol in the ratio  7 : 5. When 18 liters of mixture are drawn off and the container is filled with alcohol, the ratio becomes 7 : 9. How many liters of water was contained by the container initially?

1. 42 liters
2. 52 liters
3. 40 liters
4. 50 liters

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Correct Answer - Option 1 : 42 liters

Given:

A container contains a mixture of water and alcohol in the ratio  7 : 5

18 liters of mixture are drawn off and the container is filled with alcohol new ratio becomes 7 : 9

Concept used:

Mixture concept used

Calculation:

Let initially the container contains  7x and 5x liter of mixture of water and alcohol

⇒ Quantity of water in the container = 7x - (7/12) × 18

⇒ (7x - 21/2) liter

⇒ Quantity of Alcohol in the container = 5x - (5/12) × 18

⇒ (5x - 15/2) liter

⇒  (7x - 21/2)/[(5x - 15/2) + 18] = 7 / 9

⇒ (14x - 21)/(10x + 21) = 7 / 9

⇒ 126x - 189 = 70x + 147

⇒ 56x = 336

⇒ x = 6

∴ The quantity of water initially is  7 × 6 = 42 liter