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 2A = 3B = 4C
Now 2A = 3B
? A/B = 3/2
or A : B = 3 : 2 = (3 x 2) : (2 : 2) = 6 : 4
Again 3B = 4C
? B/C = 4/3
or B : C = 4 : 3
? A : B : C = 6 : 4 : 3
Ratio of share of A, B and C = Ratio of their investments
= 45000 : 55000 : 60000 = 9 : 11 : 12
A's share = (9/32) x 11200 = ? 3150
B's share = (11/32) x 11200 = ? 3850
? B's share more than A = ( 3850 - 3150) = ? 700
Ratio of shares of A, B and C = Ratio of their investments
= 28000 : 35000 : 14000 = 4 : 5 : 2
? A's share = (4/11) x 5225 = ? 1900
A : B = 5 : 2 = 5/2 : 1, B : C = 7 : 13 = 1 : 13/7
A : B : C = 5/2 : 1 : 13/7 = 35 : 14 : 26
? A's part = 750 x 35/75 = ? 350
Required sub - duplicate ratio of 81 : 64 = ?81 : ?64 = 9 : 8
Required triplicate ratio of 7 : 5 = 73 : 53
= 343 : 125
Required inverses ratio of 17 : 19 = (1/17) : (1/19) = 19 : 17
Given that a /b = b/c
? b2 = ac
? a4 : b4 = a4 : a2 c2 = a2 : c2
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
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