Problem Setup: Initial Mixture Ratio
Let the initial quantities of alcohol and water in the mixture be $5x$ litres and $4x$ litres, respectively, based on the given ratio of $5:4$.
Mixture Modification and New Ratio
9 litres of water is added to the mixture. The new quantities become:
- Alcohol: $5x$ litres
- Water: $(4x + 9)$ litres
The updated ratio of alcohol to water is $4:5$.
Calculating the Unknown Variable
We can set up an equation using the new ratio:
$ \frac{\text{Quantity of Alcohol}}{\text{Quantity of Water}} = \frac{4}{5} $
Substituting the quantities:
$ \frac{5x}{4x + 9} = \frac{4}{5} $
Cross-multiply to solve for $x$:
$ 5 \times (5x) = 4 \times (4x + 9) $
$ 25x = 16x + 36 $
Subtract $16x$ from both sides:
$ 25x - 16x = 36 $
$ 9x = 36 $
Divide by 9:
$ x = \frac{36}{9} = 4 $
Determining Alcohol Quantity
The initial quantity of alcohol in the mixture is $5x$ litres.
Substitute the value of $x=4$:
$ \text{Quantity of Alcohol} = 5 \times 4 = 20 \text{ litres} $
Similar Questions
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Important Questions from Mixture and Alligation
A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?
The average score of a batsman after his 50th innings was 46.4. After 60th innings, his average Score increases by 2.6. What was his average score in the last ten innings?
If 1 litre of water weighs 1 kg, then how many cubic millimeters of water will weigh 0.1 gm?
A vessel full of water weighs 4o kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?
Two equal glasses of same type are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot?
