In a mixture of three varieties of pulses, the ratio of their weight is (4 : 5 : 8). If 5 kg of the first variety, 10 kg of the second variety and some quantity of the third variety is added to the mixture, the ratio of the weights of three varieties of pulses becomes as (5 : 7 : 9). in the final mixture, find the total quantity of the third variety of pulses.

Initial ratio 4:5:8 means weights are 4k, 5k, 8k. After adding, new ratio 5:7:9 means (4k+5):(5k+10):(8k+x) = 5:7:9. From 4k+5 = 5t and 5k+10 = 7t, we get k = 5t - 5 and k = (7t-10)/5. Solving: 5t - 5 = (7t-10)/5 gives 25t - 25 = 7t - 10, so 18t = 15, t = 5/6, k = -5/3 (invalid). Alternative: 4k+5 / 5k+10 = 5/7 gives 28k+35 = 25k+50, so k = 5. Then 8k+x = 9t = 9(7/6) = 10.5, so x = 10.5 - 40 = -29.5 (invalid). Correct setup: (4k+5)/(5k+10) = 5/7 gives k=5, and (8k+x)/(5k+10) = 9/7 gives x = 45. Total third variety = 8(5) + 45 = 85. But the question asks for x only, which is 45. Option D matches x = 45.