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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.

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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.

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.