Percentages
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Q.

8 is 4% of $a$, and 4 is 8% of $b$. $c$ equals $b/a$. What is the value of $c$?

 A.

$1/32$

 B.

$1/4$

 C.

$1$

 D.

$4$

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Solution:
Option(B) is correct

4% of $a$ is $\dfrac{4a}{100}$.

Since this equals 8, we have $\dfrac{4a}{100} = 8.$

Solving for $a$ yields $a = 8×\left(\dfrac{100}{4}\right) = 200.$

Also, 8% of $b$ equals $\dfrac{8b}{100}$ and this equals 4.

Hence, we have $\left(\dfrac{8}{100}\right)× b = 4.$

Solving for $b$ yields $b = 50.$

Now, $c = \dfrac{b}{a}$

$= \dfrac{50}{200}$

$= \dfrac{1}{4}.$

Edit: For an alternative solution with less calculation, check comment from KARTIK.


(1) Comment(s)


KARTIK
 ()

one more way.

$4= 0.08b$ -------- (1)

$8= 0.04a$ -------- (2)

Divide (1) by (2),

$\dfrac{1}{4} =\dfrac{b}{a}=c$