safeer wrote:
Could you please help me out to find the easiest way to find the continued ratio of following problems?
(1) Find A:B:C:D, if A:B= 4:5 , B:C= 2:3 , and B:D= 1:7
(2) Find the continued ratio of A, B, C, and D, if A:B= 20:27 , B:C= 8:15 and C:D= 5:6
please explain the easiest way
Responding to a pm:
Conceptually, this is what you should understand:
Given two ratios
A:B = 4:5 -> this means for every 4 of A, we have 5 of B
B:C = 2:3 -> this means for every 2 of B, we have 3 of C
Now, we have B common in the two ratios so we can compare A and C. But for that, the B of both ratios should be equal. Note that when you multiply/divide a ratio by a number, the ratio does not change. 2:3 is the same as 4:6 and 6:9 and 20:30 etc.
So you multiply the first ratio by 2 and the second ratio by 5 to get
A:B = 8:10 -> for every 8 of A, we have 10 of B
B:C = 10:15 -> for every 10 of B, we have 15 of C
B takes the value of LCM of 5 and 2 i.e. 10 in both ratios. Now, A and C are comparable. For every 8 of A, we have 10 of B and for 10 of B, we have 15 of C. So for every 8 of A, we have 15 of C.
A:B:C = 8:10:15
Do the same for the remaining ratio too. B:D = 1:7
B is 10 in the ratio above so multiply this ratio by 10. You get B:D = 10:70. So for every 10 of B, you have 70 of D.
A:B:C:D = 8:10:15:70
2.
A:B= 20:27 , B:C= 8:15 and C:D= 5:6
The numbers here will be cumbersome.
Multiply first ratio by 8 and second by 27
A:B = 160:216
B:C = 216:405
Multiply the 3rd ratio by 81 to make C 405.
C:D = 405:486
Final ratio A:B:C:D = 160:216:405:486
_________________
Karishma
Veritas Prep GMAT Instructor
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