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Ratio and Proportion

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Ratio and Proportion [#permalink] New post 16 Jul 2012, 08:23
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.

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Re: Ratio and Proportion [#permalink] New post 16 Jul 2012, 09:52
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Hi,


a:b = 2/3 ; b:c=3/4 ; c:d=8/9 and d:e = 27/12

take d:e = 27/12 => d= 27*e/12 = 9e/4 ...(1)

c:d = 8/9 => c = 8*d/9 = 8 *(9e/4)/9 (substituting value of d from (1) )
=> c = 2e ....(2)

b:c = 3/4 => b =3c/4 => 3*2e/4 (substituting value of c from (2) )

=> b = 3e/2 ....(3)

a/b = 2/3 => a=2b/3 => a = 2(3e/2) / 3 (substituting value of b from (3) )

=> a = e ....(4)

From (1) , (2) , (3) and (4) we have

a:b:c:d:e = e:(3e/2):2e:(9e/4):e = 1:3/2:2:9/4:1 = 4:6:8:9:4

hope this helps!
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Re: Ratio and Proportion [#permalink] New post 16 Jul 2012, 10:44
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
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Re: Ratio and Proportion [#permalink] New post 17 Jul 2012, 21:26
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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


Given:
a:b = 2:3 and b:c = 3:4
What does the ratio a:b = 2:3 imply? It means "if a is 2, b is 3"
What does the ratio b:c = 3:4 imply? It means "if b is 3, c is 4"

What do we get from this? "if a is 2, b is 3 and c is 4"
If a:b:c = 2:3:4 and c:d = 8:9
c is not the same in both the ratios but can we make it same? Multiply the first ratio by 2. (ratio doesn't change if you multiply/divide each term by the same number)
a:b:c = 4:6:8 and c:d = 8:9
So, a:b:c:d = 4:6:8:9 and d:e = 27:12 = 9:4 (we divide the ratio by 3. It still stays the same.)
So a:b:c:d:e = 4:6:8:9:4

For more on ratios, check: http://www.veritasprep.com/blog/2011/03 ... of-ratios/
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Re: Ratio and Proportion [#permalink] New post 04 Dec 2013, 11:56
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Re: Ratio and Proportion [#permalink] New post 23 Mar 2015, 11:51
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Re: Ratio and Proportion [#permalink] New post 23 Mar 2015, 16:53
Expert's post
Hi All,

When dealing with a prompt that includes multiple ratios, it's often helpful to start with the variable that has the "weirdest" ratios attached to it. In this example, none of the ratios is that "weird", so I'd look at the variable with the "biggest" numbers attached and start there....

We're given:

A:B
2:3

B:C
3:4

C:D
8:9

D:E
27:12

D has to be a multiple of 9 and 27, so let's "lock in" that value at 27....

D = 27 so.....
E = 12

C:D
8:9

Since we "tripled" the D, we have to "triple" the C......C = 8(3) = 24

With the value of C, we can work back to figure out the B and the A
C = 24

B:C
3:4

Since we had to multiply the C by 6, we have to multiply the B by 6....

B = 3(6) = 18

A:B
2:3

Finally, we had to multiply the B by 6, so we have to multiply the A by 6....

A = 2(6) = 12

The final ratio of A:B:C:D:E is....

12:18:24:27:12

Since all of these numbers are divisible by 3, we can reduce this ratio to....

4:6:8:9:4

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Ratio and Proportion [#permalink] New post 01 Apr 2015, 23:32
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This rule is useful in Ratio & Proportion topic.

Rule of Three
The method of finding the 4th term of the proportion when the other three are known is known as the Rule of Three / Simple Proportion. Let’s understand it with an example.

Example 2: If in a particular interval of time 12 girls make 111 dolls, then how many girls should be employed for making 148 dolls?
Solution:
Rule I - ____ : ____ = ____ : Number of Girls
Rule II- ____ : ____ = 12 : X
Rule III- 111 : 148 = 12 : X
According to Rule of Three,
X = (Multiplication of Means)/ (First Term)
So, Number of girls = X = (12*148)/111 = 16

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Ratio and Proportion   [#permalink] 01 Apr 2015, 23:32
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