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# How to find continued ratio in easiest way?

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Intern
Joined: 04 Nov 2015
Posts: 6
How to find continued ratio in easiest way?  [#permalink]

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04 Nov 2015, 07:27
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

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Joined: 06 Nov 2014
Posts: 1861
Re: How to find continued ratio in easiest way?  [#permalink]

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04 Nov 2015, 20:12
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

Hi safeer,

The best way to find out the continued ratio would be by making the denominator of the first and the numerator of the next term same
A/B = 4/5, (i)
B/C = 2/3, (ii)
B/D = 1/7 (iii)

If we make the denominator and numerator of (i) and (ii) same,

We have A/B = 8/10 and B/C = 10/15
Hence, we have A:B:C = 8:10:15

Now from (iii), we can write B/D = 1/ 7 = 10/70 (making the value of B equal)

Hence A:B:C:D = 8:10:15:70

The similar technique can be applied in the 2nd question too.
Let me know if you are facing difficulties in solving the problem.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10477
Location: Pune, India
Re: How to find continued ratio in easiest way?  [#permalink]

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05 Nov 2015, 19:46
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

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

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10477
Location: Pune, India
Re: How to find continued ratio in easiest way?  [#permalink]

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05 Nov 2015, 19:59
safeer wrote:
(3) Find continued ratio. If A:B= 2/3 : 3/4 , B:C= 4/5 : 5/6 , C:D= 6/7 : 7/8

this way not works for above (3) problem. could you please solve it and explain it step by step?

Use the same method but convert the ratio into integers first for ease.

Multiply the first ratio by 12 - the LCM of 3 and 4 - to get rid of the denominators (it will not change the ratio).
A:B = (2/3) * 12 : (3/4) * 12 = 8:9

Multiply the second ratio by 30
B:C = 24:25

Multiply the third ratio by 56
C:D = 48:49

Now you have three simple ratios just like before. You can find A:B:C:D
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Karishma
Veritas Prep GMAT Instructor

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Re: How to find continued ratio in easiest way?  [#permalink]

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05 Nov 2015, 20:51
1
Quote:
(3) Find continued ratio. If A:B= 2/3 : 3/4 , B:C= 4/5 : 5/6 , C:D= 6/7 : 7/8
this way not works for above (3) problem. could you please solve it and explain it step by step?

In this case, A, B, C and D have been given in the form of fractions, so first we need to convert the ratio of A:B etc. in a proper form

A:B is nothing but A/B

Hence A:B = 2/3: 3/4 = (2/3)/ (3/4) = 2/3 * 4/3 = 8/9
Similarly, B:C = (4/5)/(5/6) = 4/5 * 6/5 = 24/25
and C:D = (6/7) / (7/8) = 6/7 * 7/8 = 3/4

From here on, you can solve it simply using the way used in the first problem.

Does it help?
Re: How to find continued ratio in easiest way?   [#permalink] 05 Nov 2015, 20:51