Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively

Quantity of A in mixture left 

= (7x - 7/12 x 9) litres = (7x - 21/4) litres.

Quantity of B in mixture left 

= (5x - 5/12 x 9) litres = (5x - 15/4) litres.

(7x - 21/4) / [(5x - 15/4)+9] = 7/9 = › 28x - 21/20x + 21 = 7/9 =› 252x - 189 = 140x + 147

     =› 112x = 336 =’ x = 3.

So, the can contained 21 litres of A.

Suppose the vessel initially contains 8 litres of liquid. Let x littres of this liquid be replaced with water.

Quantity of water in new mixture = (3 - 3x/8 + x) litres.

Quantity of syrup in new mixture = (5 - 5x/8) litres.

 (3 - 3x/8 + x) = (5 - 5x/8) = 5x + 24 = 40 - 5x 

=› 10x = 16 =› x = 8/5

So, part of the mixture replaced = (8/5 x 1/8) = 1/5.

Here, CP of unit quantity of Dearer = 460 per kg , 

CP of unit quantity of Cheaper = 410 per kg 

So we can use above formulas : 

Quantity of cheaper/Quantity of dearer =

{C.P of dearer-Mean price}/{Mean price-C.P of cheaper}

460-430/430-410=30/20=3/2

Solution : First we have to find cost price of mixture, as seller is gaining 25 % profit on mixture so its cost price will be 50=C.P of mixture *125/100=C.P of mixture=40 30/Quantity of dearer=60-40/40-25=20/15=4/3 Quantity of dearer=30*3/4=22.5Kgs

Solution : By rule of alligation 15 0 10 10-0 15-10 20/Quantity of milk=15-10/10-0 So, Quantity of milk will be 40 liters