6 liters of milk and water mixture has 75% milk in it. How much milk should be added to the mixture to make it 90% pure?

Quantity of milk @ Rs.10 per liter / Quantity of milk @ Rs. 16 per liter = 1 / 2
So, quantity of milk @ Rs. 10 per liter = 26 / 2 = 13 liter.

2nd Method
Let us assume shopkeeper buy P liter milk of price @ Rs. 10 per liter.
Buy price of 26 liter of milk @ Rs. 16 per liter = 26 x 16
Buy price of P liter of milk @ Rs. 10 per liter = P x 10
Sell price of total milk ( P + 26 ) @ Rs. 14 per liter = 14 x ( P + 26 )
According to question there is no loss or no profit.
Then Buy Price = Sell Price
26 x 16 + P x 10 = 14 x ( P + 26 )
? 26 x 16 + 10P = 14P + 14 x 26
? 26 x 16 - 26 x 14 = 14P - 10P
? 2 x 26 = 4P
? 4P = 2 x 26
? P = 2 x 26 / 4 = 13

So, quantity of milk @ Rs. 10 per liter = 13 liter.

Let us assume the ratio product is Q.
According to question,
Quantity of Milk in mixture = 6Q ml
Quantity of Water in mixture = 2Q ml
Quantity of Milk in mixture + Quantity of Water in mixture = 640
6Q + 2Q = 640
8Q = 640
Q = 640/8
Q = 80
Quantity of Milk in mixture = 6Q ml = 6 x 80 = 480 ml
Quantity of Water in mixture = 2Q ml = 2 x 80 = 160 ml
To find the new mixture containing half milk and half water,
Quantity of water to be added for making the mixture of equal quantity of milk and water = 480 - 160 = 320

According to question,
Quantity of Milk/Quantity of Water = 3/2
Let us assume the product ratio = n.
Quantity of Milk = 3n and Quantity of Water = 2n liters
Quantity of Milk + Quantity of Water = 20 liters
3n + 2n = 20 liters
5n = 20 liters
n = 20/5
n = 4
Quantity of Milk = 3n liters
Put the value of n,
Quantity of Milk = 3 x 4 = 12 liters
Quantity of Water = 2n
Quantity of Water = 2 x 4 = 8 liters
If 10 liters of mixture are removed first time, we will find how much milk and water contain in mixture.
? 20 liters of mixture contains 12 liter of milk.
? 1 liters of mixture contains 12/20 liter of milk.
? 10 liters of mixture contains 10 x 12/20 liter of milk.
? 10 liters of mixture contains 6 liter of milk.
? 10 liters of mixture contains 4 liter of water.
If 10 liters of mixture are removed, then amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters and water = 4 liters.
If the process is repeated one more time and 10 liters of the mixture are removed second time, then
If 10 liters of mixture are removed, Again we will find how much milk and water contain in the mixture.
? 20 liters of mixture contains 16 liter of milk.
? 1 liters of mixture contains 16/20 liter of milk.
? 10 liters of mixture contains 10 x 16/20 liter of milk.
? 10 liters of mixture contains 8 liter of milk.
? 10 liters of mixture contains 2 liter of water.
If 10 liters of mixture are removed, then amount of milk removed = 8 liters and amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 - 2) = 2 liters.
Now 10 liters milk is added => total milk = 18 liters and water will be 2 liters.
The required ratio of milk and water in the final mixture obtained
Quantity of milk/Quantity of Water= 18:2 = 9:1

Let cost price of spirit be Re. 1 per liter.
Then SP of mixture = Re. 1 per liter
Gain = 25%
So, CP of mixture = 1 × (100 / 125) = Re. 4 / 5
We assume that CP of water is zero.
Using allegation rule on cost price,
Water should be mixed to spirit in the ratio (1 / 5) : (4 / 5) or 1 : 4

According to figure we find that the ratio will be 3 : 1.

Quantity sold at 20% profit = 3 / (3 + 1) × 50 = 37.5 kgs.
Quantity sold at 40% profit = (50 ? 37.5) = 12.5 kgs.

As per figure we can calculate the ration as below
Number of officers / Number of workers = 1000 / 7000 = 1 / 7
No. of officers = 1 / (1 + 7) × 400 = 50
No. of workers = 400 ? 50 = 350

Total quantity of iron = 4 (1 / 4) + 6 (2 / 3) = 1 + 4 = 5 kg.
Total quantity of tin = (4 + 6) ? 5 = 5 kg.
In the resultant mixture, iron : tin = 5 : 5 or 1 : 1

Average no. of legs per head = (320 / 100) = (16 / 5)
or, 3 : 2
No. of goats = (3 / 3 + 2) × 100 = 60
No. of chickens = 100 ? 60 = 40.