This problem involves finding the initial quantity of a mixture based on initial and final ratios after adding specific amounts of components.
Ratio Mixture Initial Quantity Calculation
We are given the initial ratio of milk to water in a pot and the ratio after adding equal amounts of milk and water. We need to determine the total initial quantity.
Step 1: Define Initial Quantities using Ratio
Let the initial quantities of milk and water be $3x$ litres and $4x$ litres, respectively, based on the given ratio of 3:4.
The initial total quantity of the mixture is the sum of milk and water quantities:
$ \text{Initial Total Quantity} = 3x + 4x = 7x \text{ litres} $Step 2: Define Final Quantities after Additions
According to the problem, 10 litres of milk and 10 litres of water are added to the mixture.
- New quantity of milk = $3x + 10$ litres
- New quantity of water = $4x + 10$ litres
Step 3: Formulate the Equation using the New Ratio
The new ratio of milk to water is given as 4:5.
Therefore, we can set up the equation:
$ \frac{3x + 10}{4x + 10} = \frac{4}{5} $Step 4: Solve for 'x'
Cross-multiply the terms to solve for $x$:
$ 5(3x + 10) = 4(4x + 10) $Expand both sides:
$ 15x + 50 = 16x + 40 $Rearrange the terms to isolate $x$:
$ 50 - 40 = 16x - 15x $ $ 10 = x $So, the value of $x$ is 10.
Step 5: Calculate the Initial Total Mixture Quantity
Substitute the value of $x = 10$ back into the expression for the initial total quantity ($7x$):
$ \text{Initial Total Quantity} = 7x = 7 \times 10 = 70 \text{ litres} $The initial quantity of the total mixture was 70 litres.
Important Questions from Mixture Problems
A mixture of acid and water contains 20 percent acid. When 10 litres of water is added to the mixture, then the percentage of acid becomes 15 percent. What is the original quantity of mixture ?
A container contains 20 L mixture in which there is 10% sulphuric acid. Find the quantity of sulphuric acid to be added in it to make the solution to contain 25% sulphuric acid.
The ratio of milk to water in a 100 litres mixture is 2 ∶ 3. 10 litres of this mixture is withdrawn and replaced with milk. This process is repeated 2 more times, What is the percentage of milk in final mixture ?
- 80% and 90% pure acid solutions are mixed to obtain 20 litres of 87% pure acid solution. Find the quantity (in litres) of 80% pure acid solution taken to form the mixture.
Some fruits are bought at a rate of 11 for Rs. 100 and an equal number at a rate of 9 for Rs. 100. If all the fruits are sold at a rate of 10 for Rs. 100, then what is the gain or loss percent in the entire transaction?
