A man invested two equal sums of money in two banks at...

Let the amount invested = $P sum in two bank accounts
Interest on the first investment at 10% rate; SI = PRT/100
$$=\frac{\left(P\cdot10\cdot2\right)}{100}=\ \frac{P}{5}$$
Interest on second investment at 20% rate ; $$=\frac{\left(P\cdot20\cdot2\right)}{100}=\ \frac{2P}{5}$$
$$difference\ of\ interest\ =\frac{2p}{5}-\frac{p}{5}=\frac{p}{5}$$
$$given\ that\ 120<\frac{p}{5}<140\ =\ 600<p<700$$
Amount received on first investment at compound interest = $$p\left(1+10\%\right)^2\ =\ p\left(1+\frac{10}{100}\right)^2$$
$$=\ p\left(1+0.1\right)^2\ =\ p\left(1.1\right)^2$$
= p(1.21) = 1.21p

Amount received on second installment at compound interest = p(1+20%)^2 = p (1 + 20/100)^2
$$=\ p\left(1+0.2\right)^2\ =\ p\left(1.2\right)^2$$
$$=\ p\ \left(\ 1.44\ \right)\ =\ 1.44p$$
$$Difference\ of\ amounts\ =\ 1.44p\ -\ 1.21p\ =\ 0.23p$$
= 0.23* 600 <Difference of amounts < 0.23 * 700
= 138 < 0.23p < 161
Only option D falls within the range .
Answer = Option D