Question

Two samples of tea contain Darjeeling and Assam tea in proportion of 2:3 and 5:3 by weight. They are mixed together in proportion of 3:4 by weight. Find the proportion of Darjeeling and Assam tea in the final mixture.

Answer 1

Let us assume the final mixture has 3x weight of the first sample and 4x weight of the second sample.
Now we already know that the first sample has a proportion of 2 :3 of Darjeeling and Assam tea respectively.
Then
Amount of Darjeeling tea in first sample = (2/5) * 3x
                                                               = 6x/5
Amount of Assam tea in first sample = (3/5) * 3x 
                                                           = 9x/5
Amount of Darjeeling tea in second sample = (5/8) * 4x
                                                                      = 20x/8
Amount of Assam tea in the second sample = (3/8) * 4x
                                                                       = 12x/8
Total quantity of Darjeeling tea in both mixtures = (6x/5) + (20x/8)
                                                                             = 148x/40
Total quantity of Assam tea in both mixtures = (9x/5) + (12x/8)
                                                                        = 132x/40
The actual proportion of of Darjeeling tea and
Assam tea in the final mixture = (148x/40) : (132x/40)
                                                = 148:132
                                                = 37:33
So 37:32 is the proportion of Darjeeling tea and Assam tea respectively in the final mixture.