Given that a /b = b/c
? b2 = ac
? a4 : b4 = a4 : a2 c2 = a2 : c2
Required inverses ratio of 17 : 19 = (1/17) : (1/19) = 19 : 17
Required triplicate ratio of 7 : 5 = 73 : 53
= 343 : 125
Required sub - duplicate ratio of 81 : 64 = ?81 : ?64 = 9 : 8
Required duplicate ratio of
2 : 7 = 22 : 72 = 4 : 49
Lat the 4th proportional = N
Then, 4 : 16 : : 7 : N
? 4/16 = 7/N
? 4N = 7 x 16
? N = (7 x 16)/4 = 7 x 4 = 28
Given that, a/b = 3/5, b/c = 4/7
? a/c = a/b x b/c = 3/5 x 4/7 = 12/ 35
&there4: a : c = 12 : 35
Given that 4a = 5b
? a/b = 5/4
Also 7b = 9c
? b/c = 9/7
? a : b = 5 : 4 = (5 x 9) : (4 x 9) = 45 : 36
and b : c = 9 : 7 = (9 x 4) : (7 x 4) = 36 : 28
? a : b : c = 45 : 36 : 28
Let a/7 = b/9 = c/11 = K
Then, a = 7K, b = 9K, c = 11K
? a : b : c = 7K : 9K : 11K = 7 : 9 : 11
Given that, 30 % of A = 20 % of B
? A/B = 20/30 = 2/3
? A : B = 2 : 3
Given that, P : Q : R = 2 : 3 : 4
Let P = 2K, Q = 3K, R = 4K
? P/Q = 2K/3K = 2/3,
Q/R = 3K/4K = 3/4,
R/P = 4K/2K = 2/1
? P/Q : Q/R : R/P = 2/3 : 3/4 : 2/1
= (2 x 12)/3 : (3 x 12)/ 4 : (2 x 12)/1
= (2 x 4) : (3 x 3) : 24
= 8 : 9 : 24
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