Let C.P. of 1 litre milk be Re. 1.

S.P. of 1 litre of mixture = Re.1, Gain  =  \(\frac{50}{3}\)  %

 So, C.P. of 1 litre of mixture =  \(\left(100\times\frac{3}{350}\times1\right)=\frac{6}{7}\)

By the rule of alligation, we have:

C.P. of 1 litre of water  = 0

C.P. of 1 litre of milk =  Rs.1

Main Price = \(\frac{6}{7}\)

So, Ratio of water and milk =  \(\frac{1}{7}:\frac{6}{7}=1:6.\)

By the rule of alligation:

Cost of 1 kg of 1^st kind = 720 p

Cost of 1 kg of 2^nd kind = 570 p

Main Price = 630 p

So, Required ratio = 60 : 90 = 2 : 3.

S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%.

C.P. of 1 kg of the mixture = Rs. \(\left(\frac{100}{110}\times68.20\right)=Rs. 62.\)

By the rule of alligation, we have:

Cost of 1 kg tea of 1^st kind = Rs. 60

Cost of 1 kg tea of 2^nd kind. = Rs. 65

Main Price = Rs, 62

So, Required ratio = 3 : 2.

Let the price of the mixed variety be Rs. x per kg.

By rule of alligation, we have

Cost of 1 kg of Type 1 rice = Rs.15

Cost of 1 kg of Type 2 rice = Rs. 20

Main Price = Rs. x

So, \(\left(\frac{20-x}{x-15}\right)=\frac{2}{3}\) 

60 - 3x = 2x - 30

 5x = 90

 x = 18.

Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations = \(\left[x\left(1-\frac{8}{x}\right)^{4}\right]liters\)

So, \(\left(\frac{x\left(1-\frac{8}{x}\right)^{4}}{x}\right)=\frac{16}{81}\)

  \({\left(1-\frac{8}{x}\right)^{4}}=\left(\frac{2}{3}\right)^{4}\)

 \({\left(\frac{x-8}{x}\right)}=\frac{2}{3}\)  

3x - 24 = 2x

x = 24

By the rule of alligation, we have:

Profit on 1^st part   = 8%

Profit on 2^nd part = 18%

Main Profit = 14%

Ration of 1^st and 2^nd parts = 4 : 6 = 2 : 3

So, Quantity of 2^nd kind = \({\left(\frac{3}{5}\times1000\right)}kg=600 kg.\)