sat-dog

The correct answer is $.54$. It's given that the number $a$ is $70\%$ less than the positive number $b$. Therefore, $a=\left(1-\frac{70}{100}\right)b$, which is equivalent to $a=\left(1-0.70\right)b$, or $a=0.30b$. It's also given that the number $c$ is $80\%$ greater than $a$. Therefore, $c=\left(1+\frac{80}{100}\right)a$, which is equivalent to $c=\left(1+0.80\right)a$, or $c=1.80a$. Since $a=0.30b$, substituting $0.30b$ for $a$ in the equation $c=1.80a$ yields $c=1.80\left(0.30b\right)$, or $c=0.54b$. Thus, $c$ is $0.54$ times $b$. Note that .54 and 27/50 are examples of ways to enter a correct answer.