A merchant has 50 kg. of sugar part of which he sells at 8 % profit and the rest at 18 % profit. He gains 14 % on the whole. The quantity sold at 18 % profit is ?

Here , Ratio of milk and water in mixture of 60 litre = 2 : 1
? Quantity of milk = 2y = 40 litre
Quantity of water = y = 20 litre
If ratio of milk and water is to be 1 : 2, then in 40 litres of milk, water should be 80 litre
? Quantity of water to be added = 60 litre.

Let C.P. of 1 liter milk be Re. 1, Gain = 16 ²/₃ % = 50/3 %
and S.P. of 1 liter mixture = Re. 1
then C.P. of 1 liter mixture = (1 x (100 x 3) / 350) = Re. (6 / 7)
By the rule of alligation,
Hence, required ratio = (1/ 7) : (6 / 7) = 1 : 6

Let the price per kg of mixed variety be Rs. P;
then By the rule of alligation,
Now, (20 - P) / (P - 15) = (2 / 3)
? 60 ? 3P = 2P ? 30
? 5P = 90
? P = Rs. 18

Let capacity of the container be P liter; then
P(1 ? 1/3)⁴ = 16
? P (2 / 3)⁴ = 16
? P(16 / 81) = 16 liters
? P = 81 liters

Using the Alligation method ,
Here , C₁ = 160 paise , C₂ = 145 paise and Mean cost Price ( M ) = 154 paise
Required ratio = ( M - C₂ ) : ( C₁ - M )
? (Dearer wheat) : (Cheaper wheat) = 9 : 6
Hence , (Dearer wheat) : (Cheaper wheat) = 3 : 2