The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount on the set of the shirt and trousers is 30%, the discount offered on the trousers is = ?

Answer: Option C

Let the marked price of the shirt and trousers be Rs. x and Rs. 2x respectively.
Let the discount offered on trousers be y%
Then, Selling price of shirt
$$\begin{array}{rl}& =60\%\text{ of Rs}\text{. }x\\ & =\text{Rs}\left(\frac{60}{100}\times x\right)\\ & =\text{Rs}\text{.}\frac{3x}{5}\\ & \text{Selling price of trousers}\\ & =\left(100-y\right)\%\text{ of Rs}\text{. }2x\\ & =\text{Rs}.\left[\frac{\left(100-y\right)}{100}\times 2x\right]\\ & =\text{Rs}.\left[\frac{\left(100-y\right)x}{50}\right]\end{array}$$
Combined Selling price of shirt and trousers
$$\begin{array}{rl}& =70\%\text{ of Rs}\text{.}\left(x+2x\right)\\ & =\text{Rs}.\left(\frac{70}{100}\times 3x\right)\\ & =\text{Rs}.\frac{21x}{10}\\ & \therefore \frac{3x}{5}+\frac{\left(100-y\right)x}{50}=\frac{21x}{10}\\ & \Rightarrow \frac{130-y}{50}=\frac{21}{10}\\ & \Rightarrow 1300-10y=1050\\ & \Rightarrow y=25\end{array}$$