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
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- 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.
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Important Questions from Mixture and Alligation
A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?
The average score of a batsman after his 50th innings was 46.4. After 60th innings, his average Score increases by 2.6. What was his average score in the last ten innings?
If 1 litre of water weighs 1 kg, then how many cubic millimeters of water will weigh 0.1 gm?
A vessel full of water weighs 4o kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?
Two equal glasses of same type are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot?
