Alligation or Mixture

Total 150 liters of mixture exist.

Number of liters of water in the mixture is = 20% of 150 = 20/100 * 150 = 30 liters.

X liters of water added to the mixture to make water 25% of the new mixture.

Total amount of water becomes (30 + X) and total volume of mixture is (150 + X)

(30 + X) = 25/100 * (150 + X)

=> 120 + 4X = 150 + X

=> X = 10 liters.

Suppose a container contains X units of a liquid from which Y units are taken out and replaced by water.

After N operations, quantity of pure liquid = X ( 1 - Y / X ) ^ N units

Now, milk exist in the container is = 50 ( 1 - 5 / 50 ) ^ 3

= 50 ( 1 - 1 / 10 ) ^ 3

= 50 * 9/10 * 9/10 * 9/10

= ( 5 * 9 * 9 * 9 ) / 100

= 36.45 liters

By the rules of alligation, (expensive variety - mixture cost) : (mixture cost - cheap variety) = (250 - 200) : (200 - 150) = 50 : 50 = 1: 1 Required ratio is 1 : 1

By the rules of alligation, (expensive variety - mixture cost) : (mixture cost - cheap variety) = (58 - 46) : (46 - 34) = 12 : 12 = 1: 1 Required ratio is 1 : 1

Let Cost Price(C.P) of milk be Rs. 1 per litre. Then, Selling Price(S.P) of 1 litre of mixture = Rs. 1 Gain obtained= 20% Then, C.P of 1 litre of mixture = Rs (100/120)*1 = Rs. 5/6.

S.P of 1 kg mixture = Rs 8, Gain =25%

C.P of 1 kg mixture = Rs (100/125)*8 = Rs 6.4

Let the C.P of milk be Rs. 1 per litre.

Milk in 1-litre mixture of A=4/7 litre; Milk in 1-litre mixture of B=2/5 litre.

Milk in 1-litre mixture of C =1/2 litre.

Then,C.P of 1-litre mixture in A= Rs 4/7, C.P of 1-litre mixture in B=2/5.