If a, b, and C are greater than 0 and a is twice as large as

Question

Need Algebric solution - step by step:

If a, b, and C are greater than 0 and a is twice as large as b percent of c, then in terms of b & c, what is a percent of c?

(A)  \frac{2bc}{100}

(B)  \frac{2bc^2}{1000}

(C)  \frac{bc^2}{5000}

(D)  \frac{b^2c}{5000}

(E)  \frac{5000b}{c^2}

Bunuel · Accepted Answer

a  is twice as large as  b  percent of  c  -->  a=2c\frac{b}{100}

What is  a  percent of  c ? -->  c\frac{a}{100}=?

Multiply first equation by  \frac{c}{100}  -->  a\frac{c}{100}=\frac{c}{100}2c\frac{b}{100}  -->  c\frac{a}{100}=\frac{c^2b}{5000}

Answer: C.

AtifS · Answer

Answer: C 
 Explanation: 
We can use Word Translation to translate the wording into mathematics and Algebra to solve step by step;
 a  is twice  b  percent of  c  ==>  a = 2 * \frac{b}{100} * c = 2bc/100  --> eq-1
and 
What is  a  percent of  c ? ==>  x = \frac{a}{100} * c = a*c*\frac{1}{100}  --> eq-2
As, we know the value of  a  from the first equation eq-1 and after putting that value into eq-2, we get;
 x = \frac{2bc}{100}*c*\frac{1}{100} = \frac{bc}{50} *c*\frac{1}{100}= \frac{bc^2}{50} * \frac{1}{100} = \frac{bc^2}{5000} .
Which is option  C

jeeteshsingh · Answer

Thanks Bunuel.. I misunderstood the question's last part as What percent is a of c .... and hence I was getting 2b as the answer!

fameatop · Answer

As per me the best way to solve this question is to Pick Smart Numbers & then verify the options

rajathpanta · Answer

It is already given that a=2  (Twice as large as b%c)......  Let this be equation 1 
We need a%c in terms of b. So Multiply equation 1 with c/100 we get- ac/100=2bc^2/10000
Therefore Ans is C

mbaiseasy · Answer

b percent of c :  \frac{bc}{100} 
a is twice as large as b percent of c: a =  \frac{2bc}{100}=\frac{bc}{50}

What is a percent of c?

a percent of c:  \frac{ac}{100} = \frac{bc}{50}*\frac{c}{100}=\frac{bc^2}{5000}

Answer: C

saurabhgoel · Answer

lets say a = 10 and b=5
so as per given info. 10 = 2*5*c/100 
Which will give c = 100

substitute the value of 'b' and 'c' in in answer choices to get value 'a'.

Kinshook · Answer

Given: 
1. a, b, and C are greater than 0 
2. a is twice as large as b percent of c

Asked: In terms of b & c, what is a percent of c?

a = 2 b% c = 2bc/100 = bc/50
a% c = ac/100 = (bc/50)*c/100 = bc^2/5000

IMO C

Archit3110 · Answer

let c = 100 ; b = 10 so a = 20 a percent of c is 20 plug in values in given options optioN C matches \frac{bc^2}{5000}

hiranmay · Answer

If a, b, and c are greater than 0 and a is twice as large as b percent of c, then in terms of b & c, what is a percent of c?

(A)  \frac{2bc}{100}

(B)  \frac{2bc^2}{1000}

(C)  \frac{bc^2}{5000}  -->   correct : a is twice as large as b% of c i.e. a= 2*b%*c= 2*\frac{b}{100}*c=\frac{2bc}{100} , now a% of c = \frac{a}{100}*c=a*\frac{c}{100}=\frac{2bc}{100}*\frac{c}{100} =\frac{bc}{50}*\frac{c}{100}= \frac{bc^2}{5000}

(D)  \frac{b^2c}{5000}

(E)  \frac{5000b}{c^2}

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