Answer
$E=1.5$
$p=\$25$
Revenue: $p\times q=25\times (1000-20\times25)=12,500$
Work Step by Step
If the demand function is $q=1000-20p$ and $p=\$30$
The elasticity can be calculated as:
$E=-\frac{dq}{dp}\times\frac{p}{q}$
The derivative of the demand function is :$\frac{dq}{dp}=-20$
Therefore at the given price $E=-(-20)\times\frac{30}{1000-20\times30}=1.5$
The maximum revenue is at the price, where $E=1$
$E=20\times\frac{p}{1000-20\times p}=1$
$40p=1000$
$p=\$25$
Here, the revenue is $p\times q=25\times (1000-20\times25)=12,500$
