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16 Jul 2012, 09:23
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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
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
16 Jul 2012, 10:52
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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!
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!
ConnectTheDots
GMAT 2: 770 Q50 V47
Posts: 239
16 Jul 2012, 11:44
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gmat102012
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
