$25.5 g$ of $H_2{O}_2$ solution on decomposition gave $1.68L$ of $O_2$ at STP.  The percentage strength by weight of the solution is

balanced equation is

$2H_2{O}_2\to 2H_{2}O+O_2$ 

From the equation it is understood that two moles of $H_2{O}_2$ gives one mole of $O_2$ 

As it is known that, at STP one mole of $O_2$ occupy $22.4$ liters of volume.

So at STP,  $1.68L$ of $O_2=1.68/22.4=0.075$ moles of $O_2$  

Hence the solution contains $0.075x2=0.15$ moles of $H_2{O}_2$

The molar mass of $H_2{O}_2$ is $34g/mol$

So the decomposed mass of $H_2{O}_2$ is equal to $0.15x34=5.1g$ in $25.5 g$  solution 

Therefore 100g of solution contains $100/25.5x5.1=20$.

Hence the correct option is (C).