Question

$a$ varies directly as $b$ and varies inversely as $c$. If $a=30$ when $b=51$ and $c=36$. Then find the value of $a$ when $b=17$ and $c=18$.

• A. $50$
• B. $40$
• C. $30$
• D. $20$

Answer 1

The correct option is D $20$

$a\alpha \frac{b}{c}$

$a=\frac{kb}{c}$

when $a=30,b=51,c=36$

$30=\frac{51k}{36}$

$k=\frac{360}{17}$

So when $b=17$

$c=18$

$a=\frac{360}{17}\times \frac{17}{18}$

$a=20$