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

Question

A. 30 
B. 40 
C. 50 
D. 45 
E. 55

fluke · Answer

% Change = \frac{Bigger-Smaller}{Base}*100

1. If x>y, x is what % greater than y.
y = base; because we are trying to find "what % greater than  y "

%Increase = \frac{x-y}{y}*100

2. If x>y; y is what percent less than x;
x = base; because we are trying to find "what % smaller than  x "

%Decrease = \frac{x-y}{x}*100

***************
Coming to the question:
a= 9/11 b, then b is what percent less than (a+b)

Base=a+b 
 Bigger=a+b 
 Smaller=b

%Decrease = \frac{Bigger-Smaller}{Base}*100

%Decrease = \frac{a+b-b}{a+b}*100

%Decrease = \frac{a}{a+b}*100

a= \frac{9}{11} b

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

\frac{a}{a+b}=\frac{9}{9+11}=\frac{9}{20}

%Decrease = \frac{a}{a+b}*100 = \frac{9}{20}*100=45

Ans: "D"

meveric82 · Answer

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

fluke · Answer

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 e 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.

subhashghosh · Answer

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

amit2k9 · Answer

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.

meveric82 · Answer

Thanks every one..for the prompt support !!!

prab · Answer

For such questions, i personally prefer the substitution method.

Spidy001 · Answer

(((a+b) - b)/(a+b))*100
(1-11/20)*100
45%

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KarishmaB · Answer

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%

mniyer · Answer

a = 9b/11
a+b = 20b/11
Which gives b is 55% of a+b.

So b is 45% less than a+b

miralishabbir · Answer

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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bumpbot · Answer

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

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

Prep Toolkit

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