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
My father is presently 25 years older than me. The sum of our ages 5 years ago was 39 years. Find my present age.
Rice worth ₹43/kg and ₹67/kg are mixed with a third variety in the ratio 2 : 1 : 5. If the mixture is worth ₹96/kg, the price (in ₹) of the third variety of rice per kg will be:
42 litres of milk at ₹25 per litre is mixed with 28 litres of milk at ₹40 per litre. Find the average price of the mixture.
15 kg of ₹10 per kg wheat is mixed with 5 kg of another type of wheat to get a mixture costing ₹30 per kg. Find the price (per kg) of the costlier wheat.
If a + b + c = 0, then the value of (a² + b² + 2ab) is equal to:
