In a mixture of three varieties of tea, the ratio of their weight is 4 : 5 : 8. If 5 kg tea of the first variety, 10 kg of tea of second variety and some quantity of tea of the third variety are added together, then the ratio of weight of three variety becomes 5 : 7 : 9. In the new mixture the quantity (in kg) of the third variety of tea was:

45

The ratio of their weights = 4 : 5 : 8

The quantity added in first variety of pulses = 5 kg

The quantity added in the second variety of pulses = 10 kg

The final ratio of the weights of three varieties of pulses = 5 : 7 : 9

Let the quantity of first variety of pulses be 4x kg

Quantity of second variety of pulses = 5x kg

Quantity of third variety of pulses = 8x kg

ratio of the weights of three varieties of pulses = 5 : 7 : 9

Let the quantity added in the third variety of pulses be y kg

⇒ (4x + 5) : (5x + 10) : (8x + y) = 5 : 7 : 9      ----(1)

⇒ \(\frac{4x + 5}{ 5x + 10}\) = \(\frac{5}{7}\)

⇒ 28x + 35 = 25x + 50

⇒ 28x – 25x = 50 – 35

⇒ 3x = 15

⇒ x = 5

From equation (1)

⇒ \(\frac{(5x + 10)}{(8x + Y)}\) = \(\frac{7}{9}\)

⇒ \(\frac{35}{40 + y}\) = \(\frac{7}{9}\)

⇒ (40 + Y) = 5 × 9

⇒  y = 45 – 40 = 5

Quantity of the third variety of pulses in the final mixture = (8x + 5)

⇒ 8 × 5 + 5 = 45