In what ratio must a grocer mix sugar at 72 paise per kg with sugar at 48 paise per kg. So that by selling the mixture at

63 paise per kg he may gain	1	of his out-lay?
	6

According to question ,
Total C. P. of 200 kg of mixture = Rs. (80 × 6·75 + 120 × 8)
Total C. P. of 200 kg of mixture = Rs. 1500
Average rate = Rs. 7·50 per kg
Required rate = 120% of Rs. 7·50
Required rate = Rs. 9 per kg.

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 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

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.

The given solution has 75% milk.
Milk to be added has 100% milk.
Milk should be added to the given mixture in the ratio 15 : 10 or 3 : 2
? Quantity of milk to be added = (3 / 2) × 6 = 9 liters.