Initial Mixture Quantities
The total volume of the mixture is $595$ litres. The initial ratio of milk to water is $17:18$.
- Total parts in the ratio = $17 + 18 = 35$.
- Initial quantity of milk = $\frac{17}{35} \times 595 = 17 \times 17 = 289$ litres.
- Initial quantity of water = $\frac{18}{35} \times 595 = 18 \times 17 = 306$ litres.
Calculating Added Milk
Let $x$ be the amount of milk (in litres) that needs to be added. The quantity of water remains unchanged.
- New quantity of milk = $289 + x$ litres.
- Quantity of water = $306$ litres.
- The desired final ratio of milk to water is $3:2$.
We can set up the equation based on the final ratio:
$ \frac{\text{New Milk Quantity}}{\text{Water Quantity}} = \frac{3}{2} $
$ \frac{289 + x}{306} = \frac{3}{2} $
Solving for Added Milk
To find the value of $x$, we solve the equation:
- Cross-multiply: $2 \times (289 + x) = 3 \times 306$.
- Simplify: $578 + 2x = 918$.
- Isolate the term with $x$: $2x = 918 - 578$.
- Calculate the difference: $2x = 340$.
- Solve for $x$: $x = \frac{340}{2} = 170$.
Therefore, $170$ litres of milk must be added.
Important Questions from Mixture Problems (Notes)
- A has a container containing 60 litres of pure milk. He takes out 4 litres of milk and replaces it with the same quantity of water. He sells this mixture to B. B sells 30 litres of the mixture and added 5 litres of water in the remaining mixture. The ratio of milk to water in the remaining mixture is:
- How many liters of water should be added to a 30-liter mixture containing milk and water in the ratio 7:3 such that the resultant mixture has 40% water in it?
- Alloy A is formed by mixing iron (Fe) and nickel (Ni) in the ratio 3:4, while alloy B is formed by mixing Fe and Ni in the ratio 9:5. If equal quantities of alloys A and B are melted together to form a new alloy C, what will be the ratio of Fe to Ni in the alloy C?
Suppose a tap mixes hot water and cold water in a ratio that depends linearly on the proportion of opening. Water out of the tap has temperature 40°C when the tap is half-open, and 30°C when it is three-fourths open. To get water at 50°C, the tap should be_______________.
- In 80 litres mixture of milk and water, the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?
