To convert a 800mV range milli-voltmeter of resistance 40Ω into a milli ammeter of 100 ma range, the resistance to be connected as shunt is,

Let's use r to represent the shunt resistance. We know that for the voltmeter to become an ammeter, the resistance connected must be in parallel with the voltmeter resistance. Therefore,
$R_{net}=\frac{40\times R}{40+R}$
Thus the current in voltmeter = ammeter.
$\Rightarrow \frac{800}{{\displaystyle \frac{40R}{40+R}}}=100$

$\Rightarrow 320+8R=40R$ 
$\Rightarrow 32R=320$
$\Rightarrow R=10\Omega$ 
Hence the correct answer is $10\Omega .$