$\%$ for ${\mathrm{CO}}_2$

$\because 0.765 \mathrm{g}$ of acid gives ${\mathrm{CO}}_2=0.535 \mathrm{g}$

$\therefore 100 \mathrm{g}$ of acid gives ${\mathrm{CO}}_2=\frac{0.535\times 100}{0.765}$

$\%$ of ${\mathrm{CO}}_2=70.00$

$\%$ for carbon 

$\because 44 \mathrm{g}$ of ${\mathrm{CO}}_2$ gives, $\mathrm{C}=12 \mathrm{g}$

$\therefore 70 \mathrm{g}$ of ${\mathrm{CO}}_2$ gives, $\mathrm{C}=\frac{12\times 70}{44}$

$=19.09 \mathrm{g}$

$\therefore \%$ of carbon $=19.00$

Similarly, 

(i) for hydrogen 

$\%$ of ${\mathrm{H}}_2\mathrm{O}$

$\Rightarrow \frac{0.138\times 100}{0.765}$

$=18.03=18.00$

$\%$ of Hydrogen

$\Rightarrow \frac{2\times 18}{18}=2.00$

Hence ratio of carbon and hydrogen is $19:2$