If the discount of 10% is given on the marked price of a radio, the gain is 20%. If the discount is increased to 20%, the gain per cent is :

Let the C.P. of article be Rs. 100 and the marked price be Rs. x. Case I $\frac{x \times 90}{100}=120$ $\Rightarrow x=\frac{120 \times 100}{90}=$ Rs. $\frac{400}{3}$ Case II S.P. $=\frac{x \times 80}{100}=$ Rs. $\frac{4 x}{5}$ $=$ Rs. $\left(\frac{4}{5} \times \frac{400}{3}\right)=$ Rs. $\frac{320}{3}$ $\therefore \quad$ Profit $=\operatorname{Rs} .\left(\frac{320}{3}-100\right)$ $=\operatorname{Rs} .\left(\frac{320-300}{3}\right)=$ Rs. $\frac{20}{3}$ $\therefore$ Profit percent $=\frac{20}{3} \%=6 \frac{2}{3} \%$ Alternative: Fraction of $10 \%=\frac{10}{100}=\frac{1}{10}$ Fraction of $20 \%=\frac{20}{100}=\frac{1}{5}$ According to the question,

Now required gain $\%=\frac{1}{15} \times 100$

$=\frac{20}{3}=6 \frac{2}{3} \%$