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

### Concept & Weighted Average The total discount percentage on a set of items is the weighted average of the discount percentages on the individual items, weighted by their respective marked prices. $$ \text{Total Discount} = \frac{(\text{MP}_1 \times D_1\%) + (\text{MP}_2 \times D_2\%)}{\text{MP}_1 + \text{MP}_2} $$ ### Step-by-Step Solution * Let the marked price of the shirt be $100x$ and the marked price of the trousers be $200x$ (since the ratio is 1 : 2). * Total marked price of the set = $100x + 200x = 300x$. * The shopkeeper gives a 40% discount on the shirt. Discount on shirt = $40\% \text{ of } 100x = 40x$. * The total discount on the set is 30%. Total discount amount = $30\% \text{ of } 300x = 90x$. * The discount on the trousers is the remaining total discount: $90x - 40x = 50x$. * The percentage discount on the trousers = $\frac{50x}{200x} \times 100$. * $\frac{50}{200} \times 100 = 25\%$. ### Exam Strategy & Shortcut Use the method of alligation or weighted averages directly on the ratios. Ratio of MP (Shirt : Trousers) = 1 : 2. Let the discount on trousers be $x\%$. $1(40) + 2(x) = 3(30)$ $40 + 2x = 90$ $2x = 50$ $x = 25\%$ ### Common Pitfall Simply averaging the discounts (e.g., trying to find a midpoint between 40% and 30% without accounting for the 1:2 weight of the marked prices) will lead to an incorrect result. ### Final Answer Therefore, the correct answer is **25%**.