Three varieties of rice taken in the ratio 3 : 4 : 5 are mixed. If 5 kg rice of first variety, 10 kg rice of second variety and some rice of third variety are added to the mixture, the ratio of the three varieties becomes 5 : 7 : 9. Find the quantity of the third variety of rice in the final mixture.

90 kg

Three varieties of rice A, B and C are mixed in ratio of 3x : 4x : 5x

5 kg rice of A, 10 kg rice of B and y kg of C are added to the mixture.

New Ratio A:B:C = (3x + 5) : (4x + 10) : (5x + y) = 5 : 7 : 9

(3x + 5) : (4x + 10) = 5 : 7

7(3x + 5) = 5(4x + 10)

21x + 35 = 20x + 50

x = 15 kg

Also, (4x + 10) : (5x + y) = 7 : 9

9(4x + 10) = 7(5x + y)

36x + 90 = 35x + 7y

x + 90 = 7y

15 + 90 = 7y

y = 105/7 = 15

The quantity of the third variety of rice in the final mixture = 5x + y = 5*15 + 15 = 90

The correct answer is Option (3) → 90 kg