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meveric82
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meveric82
Thank you very much for the help provided...

One last query: how come-

a / (a+b) = 9/(9+11), how come a=9? note- a/b= 9/11 ; doesnt mean that a=9

Pls do clarify this doubt

Invertendo/Componendo rule:

\(\frac{a}{b}=\frac{9}{11}\)

\(\frac{b}{a}=\frac{11}{9}\) --Invertendo

\(\frac{a+b}{a}=\frac{11+9}{9}=\frac{20}{9}\) --Componendo

\(\frac{a}{a+b}=\frac{9}{20}\) --Invertendo

Note: \(a \ne 9.\) \(\frac{a}{a+b}=\frac{9}{20}\)

Please go through:
math-number-theory-percents-91708.html

math-number-theory-88376.html
Ratios and Proportions.
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So {(a+b) - b}/((a+b) * 100 = ?

= a/(a+b) * 100

Now a/b = 9/11

=> b/a = 11/9

=> (a+b)/a = 20/9
=> Answer = 9/20 * 100 = 45

Answer - D
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meveric82
If a= 9/11 b, then b is what percent less than (a+b) ?

a. 30 b. 40 c.50 d. 45 e. 55

ans(as per my friend) = 45 %....


Can any one guide me W.R.T steps involved ? Need help

Let b = 11 => a = 9

a+b = 20 => b = (11/20) * 100 = 55 %
i.e, b = 45% of (a+b)

Hence IMO D.
thank you.
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Thanks every one..for the prompt support !!!
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For such questions, i personally prefer the substitution method.
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(((a+b) - b)/(a+b))*100
(1-11/20)*100
45%

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meveric82
If a= 9/11 b, then b is what percent less than (a+b) ?

a. 30 b. 40 c.50 d. 45 e. 55

ans(as per my friend) = 45 %....


Can any one guide me W.R.T steps involved ? Need help

Note that in Problem Solving questions (they have a single correct answer), the answer will be the same for every value of a and b that satisfy the given conditions. So quickest would be to assume some easy values for a and b.

Here our only condition is a = (9/11)*b
So the simplest values that satisfy this condition are b = 11 and a = 9.
In that case a + b = 20
b (11) is '9' less than a+b (20) giving us 9/20 = 45%
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meveric82
If a= 9/11 b, then b is what percent less than (a+b) ?

a. 30 b. 40 c.50 d. 45 e. 55

ans(as per my friend) = 45 %....


Can any one guide me W.R.T steps involved ? Need help
a = 9b/11
a+b = 20b/11
Which gives b is 55% of a+b. [11/20*100]

So b is 45% less than a+b
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b = (x/100) (a+b)
=> a = 9/11 b

b = (x/100) ( 9/11b + b)
Solving this will get you
11/20 = x/100
X = 55
Now in question he has asked for percent less than (a+b)
So 100-55 = 45
D is the correct answer!

Give me kudos if it helped you :)

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