gmat102012 wrote:

Hi Guys,

Need help in understanding a simple concept in Ratio & Proportion. Here it goes:

If a:b = 2/3 ; b:c=3/4 ; c:d=8/9 and d:e = 27/12, then what is the ratio of a:b:c:d:e ??

Thanks a lot.

Cheers

Simplify the fractions and start with the largest:

d/e=27/12 = 9/4

Now your task is to make alternate numerator and denominator same, so that they cancel out on multiplication.

so we already have

1. d/e =9/4

2. c/d=8/9

3. b/c=3/4=6/8

4. a/b=2/3=4/6

Mark - this has made the value of my variables same in all the ratios:

a=4 (from 4)

b=6 (from 4 and 3)

c=8 (from 3 and 2)

d=9 (from 2 and 1)

e=4 (from 1)

=> a:b:c:d:e = 4:6:8:9:4

Alternatively, quick way to find is:

a/e = (a/b) x (b/c) x (c/d) x (d/e) X (e/e)

= (2/3) X (3/4) x (8/9) x (27/12) X (1/1)

= (12/18) x (18/24) x (24/27) x (27/12) x (12/12) -> starting from the biggest make the adjacent non-paired numbers ( not within braces) equal, while maintaining the ratio

Take the numerators

12:18:24:27:12

Cancel common factors

4:6:8:9:4

_________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well."

― Voltaire

Press Kudos, if I have helped.

Thanks!