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

Options

A. `15%`
B. `20%`
C. `25%`
D. `30%`

Answer

To solve the problem step by step, we will follow the information given in the question and use the ratios and percentages to find the discount on the trousers.

### Step 1: Define the Marked Prices
Let the marked price of the shirt be \( S \) and the marked price of the trousers be \( T \). According to the problem, the ratio of the marked prices is given as:
\[ S : T = 1 : 2 \]
This means we can express the marked prices as:
\[ S = 100 \quad \text{and} \quad T = 200 \]

### Step 2: Calculate the Total Marked Price
The total marked price of the shirt and trousers combined is:
\[ \text{Total Marked Price} = S + T = 100 + 200 = 300 \]

### Step 3: Calculate the Discount on the Shirt
The shopkeeper gives a 40% discount on the shirt. Therefore, the discount amount on the shirt is:
\[ \text{Discount on Shirt} = 40\% \text{ of } S = 0.40 \times 100 = 40 \]

### Step 4: Calculate the Selling Price of the Shirt
The selling price of the shirt after the discount is:
\[ \text{Selling Price of Shirt} = S - \text{Discount on Shirt} = 100 - 40 = 60 \]

### Step 5: Calculate the Total Discount on the Set
The total discount on the set of shirt and trousers is given as 30%. Therefore, the total discount amount is:
\[ \text{Total Discount} = 30\% \text{ of Total Marked Price} = 0.30 \times 300 = 90 \]

### Step 6: Calculate the Selling Price of the Set
The selling price of the entire set (shirt + trousers) after the total discount is:
\[ \text{Selling Price of Set} = \text{Total Marked Price} - \text{Total Discount} = 300 - 90 = 210 \]

### Step 7: Calculate the Discount on the Trousers
Now, we know the selling price of the shirt is 60. Therefore, the selling price of the trousers can be calculated as:
\[ \text{Selling Price of Trousers} = \text{Selling Price of Set} - \text{Selling Price of Shirt} = 210 - 60 = 150 \]

### Step 8: Calculate the Discount on the Trousers
The marked price of the trousers is 200. The discount on the trousers can be calculated as:
\[ \text{Discount on Trousers} = T - \text{Selling Price of Trousers} = 200 - 150 = 50 \]

### Step 9: Calculate the Percentage Discount on the Trousers
Finally, to find the percentage discount on the trousers:
\[ \text{Percentage Discount on Trousers} = \left( \frac{\text{Discount on Trousers}}{T} \right) \times 100 = \left( \frac{50}{200} \right) \times 100 = 25\% \]

### Final Answer
The discount offered on the trousers is **25%**.

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