Initial Mixture Analysis
The total volume of the mixture is $72$ L.
The initial ratio of water to milk is $4 : 5$.
The sum of the ratio parts is $4 + 5 = 9$.
Calculate the quantity of each component:
- Water = $\frac{4}{9} \times 72 \text{ L} = 4 \times 8 \text{ L} = 32 \text{ L}$
- Milk = $\frac{5}{9} \times 72 \text{ L} = 5 \times 8 \text{ L} = 40 \text{ L} $
The initial quantities are $32$ L of water and $40$ L of milk.
Calculating Milk to Add
Let the amount of milk to be added be $x$ L.
The quantity of water remains constant: $32$ L.
The new quantity of milk will be $(40 + x)$ L.
The target ratio of water to milk is $3 : 6$, which simplifies to $1 : 2$.
Set up the equation based on the target ratio:
$ \frac{\text{Water}}{\text{New Milk}} = \frac{1}{2} $
$ \frac{32}{40 + x} = \frac{1}{2} $
Solving for Added Milk
Cross-multiply to solve for $x$:
$ 32 \times 2 = 1 \times (40 + x) $
$ 64 = 40 + x $
Isolate $x$:
$ x = 64 - 40 $
$ x = 24 $
Therefore, $24$ L of milk needs to be added.
Similar Questions
- A sample of milk from a vessel contains 4% water. What quantity of pure milk should be added to 8 L of milk in the vessel to reduce the water content to 2%?
- A sample of milk contains 5% of water. What quantity of pure milk should be added to 10 L of milk sample to reduce this to 2%?
- Geeta is decorating the cover of her school magazine. She is allowed to use only three colours from a group of six colours (P, Q, R, S, T and U), based on the following conditions.
I. If P, Q or R is chosen, U cannot be chosen.
II. Either T or U must be chosen.
III. S and Q cannot be chosen together.
If R is chosen, which of the following pairs of colours must also be chosen? - How much of an $80\%$ orange juice drink must be mixed with 36 litres of a $25\%$ orange juice drink to obtain a mixture that has $60\%$ orange juice?
- A mixture contains alcohol and water in the ratio of $5 : 4$. If 9 litres of water is added to the mixture, the ratio of alcohol to water becomes $4 : 5$. Find the quantity of alcohol in the mixture.
- In mixture A, there is 5 L of syrup in 6 L of water. In mixture B, there is 3.5 L of syrup in 5.5 L of water. In which of the two mixtures is the concentration of syrup greater?
- In a mixture of milk and water of 120 litres, the ratio of milk to water is $2:1$. If the ratio of milk to water needs to be $1:2$, then the amount of water that needs to be added to the mixture is:
- A milkman mixes 10% water in pure milk but he is not content with it. So, he again mixes 10% more water in the previous mixture. What is the profit percentage of milk if he sells it at cost price?
- In a stock of two products A and B initially 80% of the total stock was product A. If 20 kg of product A and 8 kg of product B were taken out from the stock, then the ratio of the product A to product B in the stock changed to 9 : 2. What was the total stock (in kg) in the beginning?
- 85L of a mixture contains milk and water in the ratio 27 : 7. How much more water should be added to get a new mixture containing milk and water in the ratio 3 : 1?
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:
