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