Initial Mixture Composition
The initial mixture has a total volume of 40 litres.
The ratio of acid to water is $3:1$. The total parts are $3 + 1 = 4$.
- Initial quantity of acid = $\frac{3}{4} \times 40 = 30$ litres.
- Initial quantity of water = $\frac{1}{4} \times 40 = 10$ litres.
Mixture Removed
8 litres of the mixture are removed.
The removed portion also has the ratio $3:1$.
- Acid removed = $\frac{3}{4} \times 8 = 6$ litres.
- Water removed = $\frac{1}{4} \times 8 = 2$ litres.
Mixture Remaining
After removing 8 litres:
- Acid remaining = $30 - 6 = 24$ litres.
- Water remaining = $10 - 2 = 8$ litres.
Replacement Solution
8 litres of a new solution are added. The ratio of acid to water in this new solution is $1:3$.
The total parts are $1 + 3 = 4$.
- Acid added = $\frac{1}{4} \times 8 = 2$ litres.
- Water added = $\frac{3}{4} \times 8 = 6$ litres.
Final Mixture Calculation
The final quantities are calculated by adding the remaining and added amounts.
- Final quantity of acid = $24 + 2 = 26$ litres.
- Final quantity of water = $8 + 6 = 14$ litres.
Final Ratio Determination
The final ratio of acid to water is the ratio of their final quantities.
Final Ratio = Final Acid : Final Water = $26 : 14$.
Simplifying this ratio by dividing both numbers by their greatest common divisor, which is 2:
Simplified Ratio = $\frac{26}{2} : \frac{14}{2} = 13 : 7$.
Similar Questions
- A bucket has 60 litres of a solution with sugar and water in the ratio 5:1. If 12 litres of the solution are replaced with water, what is the new ratio?
- A can contains 40 litres of oil at Rs. 50/litre. Another can contains 60 litres of oil at Rs. 60/litre. They are mixed, and 20 litres are sold at Rs. 70/litre. How much profit or loss does the seller make on this sale?
- A seller mixes two varieties of rice costing Rs. 40/kg and Rs. 60/kg in a certain ratio and sells the mixture at Rs. 55/kg, gaining 10%. What is the ratio in which the two types are mixed?
- A mixture of 150 litres contains acid and water in the ratio 2:3. If 30 litres of the mixture is replaced with water, what will be the percentage of acid in the final mixture?
- A chemist prepares 60 liters of antiseptic solution by mixing two liquids 'A' and 'B' in the ratio 2:3. If the cost of 'A' is Rs. 45/liter and 'B' is Rs. 30/liter, what is the average cost per liter of the final solution?
- An alloy contains tin and copper in the ratio 5:3. A second alloy contains tin and copper in the ratio 3:1. What quantity of the first alloy must be mixed with 20 kg of the second alloy to produce a new alloy with tin and copper in the ratio 4:2?
- A 45-litre mixture of kerosene and diesel contains kerosene and diesel in the ratio 4:5. How much diesel must be added to make the ratio 4:6?
- A tank contains 120 litres of liquid, 30% of which is alcohol. If 30 litres of this mixture is replaced by another liquid containing 50% alcohol, what is the percentage of alcohol in the resulting solution?
A container has 60 litres of a mixture of acid and water in the ratio 7:3. 20% of the mixture is taken out and replaced with water. This operation is repeated once more. What is the final percentage of acid in the mixture?
- A 30-litre container of pure milk undergoes a 6-litre removal and 6-litre water replacement process, repeated 4 times. Approximately how much original milk remains?
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:
