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If a:b is 2:3, b:c is 4:5 and c:d is 6:7, find the ratio of a:b:c:d

A. 2 : 3 : 4 : 5
B. 4 : 5 : 6 : 7
C. 2 : 3 : 6 : 7
D. 2 : 12 : 30 : 7
E. 16 : 24 : 30 : 35 --> correct
Solution:
a/b = 2/3, b/c = 4/5 & c/d = 6/7
=> a= 2b/3, b = 4c/5 & c = 6d/7 ---(i)
=> b = 4c/5 = (4/5)(6d/7) ---(ii) from (i)
=>a = 2b/3=(2/3)(4/5)(6d/7)---(iii) from (ii)

a:b:c:d = (2/3)(4/5)(6d/7):(4/5)(6d/7): 6d/7 : d = (2*4*6)/(3*5*7): (4*6)/(5*7):6/7:1=(2*4*6*2)/(3*5*7): (4*6)/(5*7):6/7:1
=> a:b:c:d = 2*4*2: (4*6)*(5*7)/(5*7):6*(5*7)/7:1*5*7---multiply by 5*7
=> a:b:c:d = 16: 24:30:35
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If a:b is 2:3, b:c is 4:5 and c:d is 6:7, find the ratio of a:b:c:d

A. 2 : 3 : 4 : 5
B. 4 : 5 : 6 : 7
C. 2 : 3 : 6 : 7
D. 2 : 12 : 30 : 7
E. 16 : 24 : 30 : 35

A:B = 2:3
B:C = 4:5
C:D = 6:7

B has to be multiple of 3 and 4. So at least 12. We are down to D and E.

Since C has to be 30 in both cases, D will have to be multiplied by 5. So 7*5=35. No other way to work it out.

Option E.
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