Question

Suppose $a=\frac{2}{3}b,b=\frac{2}{3}c$ and $c=\frac{2}{3}d$, what would be the value of $b$ as a fraction of $d$ ?

• A. $\frac{2}{3}$
• B. $\frac{4}{3}$
• C. $\frac{4}{9}$
• D. $\frac{8}{27}$

Answer 1

The correct option is C $\frac{4}{9}$

According to the question,

$c=\frac{2}{3}$$d$ and $b=\frac{2}{3}c$ -equation$1$

$d=\frac{3}{2}c$ -equation$2$

and from eqaution1 $c=\frac{3}{2}b$ -equation$3$

from the eqaution $2$ and $3$

$d=\frac{3\times 3}{2\times 2}b=\frac{9}{4}b$

$b=\frac{4}{9}d$

hence $b$ is the fraction of $d$ is $\frac{4}{9}$