A solution contains 30L of pure milk. 10% of his this is taken out. Another 15% of the remaining solution is taken out and finally 20% of the contents left is taken out. The total content taken out replaced with water. Find the ratio of water to milk in the final solution.

Solution

Quantity of milk = 30L When 10% solution is taken out = (10/100) ×  30 = 3 L Remaining solution = 30 L - 3 L = 27 L Now, again 15% of solution is taken out = (15/100) ×  27 = 4.05 L Remaining solution = 27 L - 4.05 L = 22.95 L Now, further 20% of solution is taken out = (20/100) ×  22.95 = 4.59 L Remaining solution = 22.95 L - 4.59 L = 18.36 L Total quantity taken out which is replaced by water = 30 L - 18.36 L = 11.64 L Required ratio = 11.64 : 18.36 = 582:918 = 291:459 = 97:153 ALTERNATE METHOD: Quantity of Milk in final remaining mixture = 30 ×  [1 - (10/100)] ×   [(1 - (15/100)] × [ (1 - (20/100)] = 30 ×  0.9 ×  0.85 ×  0.8 = 18.36 Total quantity taken out which is replaced by water = 30 L - 18.36 L = 11.64 L Required ratio = 11.64 : 18.36 = 582:918 = 291:459 = 97:153