A mixer is sold at discount of `25%` and profit given is `20%` . Find the ratio of CP to MRP.

Options

A. `5 : 8`
B. `8 : 5`
C. `4 : 5`
D. `5 : 4`

Answer

To solve the problem of finding the ratio of Cost Price (CP) to Marked Price (MRP) given a discount of 25% and a profit of 20%, we can follow these steps:

### Step 1: Understand the terms
- Let MRP = Marked Price
- Discount = 25% of MRP
- Selling Price (SP) = MRP - Discount
- Profit = 20% of CP

### Step 2: Express Selling Price in terms of MRP
Since the discount is 25%, we can express the Selling Price (SP) as:
\[ SP = MRP - (25\% \text{ of } MRP) \]
\[ SP = MRP - 0.25 \times MRP \]
\[ SP = 0.75 \times MRP \]

### Step 3: Express Selling Price in terms of CP
Since the profit is 20%, we can express the Selling Price (SP) in terms of CP as:
\[ SP = CP + (20\% \text{ of } CP) \]
\[ SP = CP + 0.20 \times CP \]
\[ SP = 1.20 \times CP \]

### Step 4: Set the two expressions for SP equal to each other
From Steps 2 and 3, we have:
\[ 0.75 \times MRP = 1.20 \times CP \]

### Step 5: Rearrange to find the ratio of CP to MRP
To find the ratio of CP to MRP, we can rearrange the equation:
\[ \frac{CP}{MRP} = \frac{0.75}{1.20} \]

### Step 6: Simplify the ratio
Now, simplify the fraction:
\[ \frac{CP}{MRP} = \frac{0.75}{1.20} = \frac{75}{120} \]
To simplify \( \frac{75}{120} \), we can divide both the numerator and the denominator by 15:
\[ \frac{75 \div 15}{120 \div 15} = \frac{5}{8} \]

### Conclusion
Thus, the ratio of CP to MRP is:
\[ \frac{CP}{MRP} = \frac{5}{8} \]

### Final Answer
The ratio of CP to MRP is **5:8**.

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