Given the three mixtures ratio as (1:2),(2:3),(3:4) (1+2),(2+3),(3+4) Total content = 3,5,7   Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105 105/3 = 35 , 105/5 = 21 , 105/7 = 15   Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)  i.e (35,70), (42,63), (45,60)   So overall mixture ratio of milk and water is 35+42+45 : 70+63+60 122:193   But in the question asked the ratio of water to milk = 193 : 122

Given the three mixtures ratio as (1:2),(2:3),(3:4) (1+2),(2+3),(3+4) Total content = 3,5,7   Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105 105/3 = 35 , 105/5 = 21 , 105/7 = 15   Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)  i.e (35,70), (42,63), (45,60)   So overall mixture ratio of milk and water is 35+42+45 : 70+63+60 122:193   But in the question asked the ratio of water to milk = 193 : 122

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.   By rule of alligation we have required ratio X:Y       X                  :                 Y     4/7                                2/5              \                      /               (Mean ratio)                   (1/2)             /                      \  (1/2 ? 2/5)     :       (4/7 ? 1/2)       1/10                      1/1 4    So Required ratio = X : Y = 1/10 : 1/14 = 7:5

Initial quantity of copper = 80 100   x   50 = 40 g  And that of Bronze = 50 - 40 = 10 g Let 'p' gm of copper is added to the mixture => 50   +   p   x   90 100 = 40 + p => 45 + 0.9p = 40 + p => p = 50 g Hence, 50 gms of copper is added to the mixture, so that the copper is increased to 90%.

Given rate of wheat at cheap = Rs. 2.90/kg Rate of wheat at cost = Rs. 3.20/kg Mixture rate = Rs. 3/kg Ratio of mixture =            2.90                              3.20                               3 (3.20 - 3 = 0.20)            (3 - 2.90 = 0.10)   0.20 : 0.10 = 2:1   Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.

Given rate of wheat at cheap = Rs. 2.90/kg Rate of wheat at cost = Rs. 3.20/kg Mixture rate = Rs. 3/kg Ratio of mixture =            2.90                              3.20                               3 (3.20 - 3 = 0.20)            (3 - 2.90 = 0.10)   0.20 : 0.10 = 2:1   Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.

From the given data,   The part of honey in the first mixture = 1/4   The part of honey in the second mixture = 3/4   Let the part of honey in the third mixture = x   Then,   1/4             3/4              x   (3/4)-x     x-(1/4)    Given from mixtures 1 & 2 the ratio of mixture taken out is 2 : 3   =>  3 4 - x x - 1 4 = 2 3   => Solving we get the part of honey in the third mixture as 11/20   => the remaining part of the mixture is water = 9/20   Hence, the ratio of the mixture of honey and water in the third mixture is 11 : 9 .

As water costs free, water sold at cost price of milk gives the profit. Required profit % = 5/20 x 100 = 5 x 5 = 25%.

Let he mixes the oils in the ratio = x : y Then, the cost price of the oils = 60x + 65y Given selling price = Rs. 68.20 => Selling price = 68.20(x+y) Given profit = 10% = SP - CP => 10/100 (60x + 65y) = 68.20(x+y)-(60x + 65y) => 6x + 6.5y = 8.20x + 3.20y =>2.2x = 3.3y => x : y = 3 : 2

As given equal amounts of alloys are melted, let it be 1 kg. Required ratio of gold and silver =  5 13   +   5 8 8 13   +   3 8   =   105 103 .   Hence, ratio of gold and silver in the resulting alloy = 105/103.