Question

The ratio compounded of the duplicate ratio of 4 : 5, triplicate ratio of 1 : 2, sub duplicate ratio of 81 : 256 and sub triplicate ratio of 125 : 512 is a) 4 : 512 b) 3 : 32 c) 1 : 120 d) None of these

Answer 1

Answer:

1/120

Step-by-step explanation:

The duplicate ratio of 4 : 5 is 4^2 : 5^2 i.e. 16 : 25

The triplicate ratio of 1 : 3 is 1^3 : 3^3 = 1 : 27

Sub duplicate ratio of 81 : 256 is (81)^1/2 : (256)^1/2 i.e. 9 : 16

Sub triplicate ratio of 125 : 512 is (125)^1/3: (512)^1/3 i.e. 5 : 8

Therefore the compounded ratio of (16:25) ; (1:27); (9:16) and (5:8) is:

16/25 x 1/27 x 9/16 x 5/8 = 9 x 5/25 x 27 x 8 = 1/(5 x 3 x 8) = 1/120.