Problem Solving

BTGmoderatorLU wrote:a percent of b is c and c percent of d is e, then a is what percent of e? (a, b, c, d, e > 0)

A. (bd)/1000
B. 10000/(bd)
C. 10000 bd
D. (bd)/10000
E. 1000000/(bd)

The OA is E.

Please, can anyone assist me with this PS question? I need help to solve it. Thanks!

Let's convert the phrase, "a percent of b is c and c percent of d is e," into math.

Given:

a% of b = c => a% x b = c => (a/100)*b = c => ab = 100c --- (1)
c% of d = e => c% x d = e => (c/100)*d = e => cd = 100e --- (2)

We have to find out a is what percent of e.
Say a is p percent of e

Then a = p% of e => a = (p/100)*e => p = 100(a/e) ---(3)

From equation #1, ab = 100c, we have a = 100c/b ---(4)
From equation #2, cd = 100e, we have e = (cd)/100 ---(5)

Dividing (3) by (4), we get

a/e = (100c/b) / [(cd)/100]

a/e = 10000/(bd)

=> 100(a/e) = 1000000/(bd)

=> p = 1000000/(bd)

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorLU wrote:a percent of b is c and c percent of d is e, then a is what percent of e? (a, b, c, d, e > 0)

A. (bd)/1000
B. 10000/(bd)
C. 10000 bd
D. (bd)/10000
E. 1000000/(bd)

We are given that:

a/100 x b = c

and

c/100 x d = e

We are asked to determine the value of a/e x 100.

Since c = a/100 x b, we can substitute this for c in c/100 x d = e and obtain:

(a/100 x b)/100 x d = e

ab/10000 x d = e

ab/10000 = e/d

a = e/d x 10000/b

a/e = 1/d x 10000/b

So:

a/e x 100 = 1/d x 10000/b x 100 = 100/d x 10000/b = 1,000,000/(bd)

Answer: E