A shopkeeper organizes sale on Friday, offering a discount of 23% on all items. Still, he makes a profit of 10% only. By how muchpercentage CP was lower than MP?

Options

A. `20%`
B. `10%`
C. `15%`
D. `30%`

Answer

To solve the problem step by step, we need to determine how much lower the Cost Price (CP) is compared to the Market Price (MP) based on the given discount and profit percentages.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Discount offered = 23%
- Profit made = 10%

2. **Define the Market Price (MP):**
- Let's assume the Market Price (MP) is 100 (this simplifies calculations).

3. **Calculate the Selling Price (SP):**
- The Selling Price (SP) after applying the discount can be calculated as:
\[ SP = MP - \text{Discount} = 100 - 23\% \text{ of } 100 = 100 - 23 = 77 \]

4. **Relate Selling Price to Cost Price:**
- Since the shopkeeper makes a profit of 10%, we can express the Selling Price (SP) in terms of Cost Price (CP):
\[ SP = CP + 10\% \text{ of } CP = CP + 0.1 \times CP = 1.1 \times CP \]
- From the previous step, we know that SP = 77. Therefore:
\[ 1.1 \times CP = 77 \]

5. **Calculate the Cost Price (CP):**
- To find CP, we rearrange the equation:
\[ CP = \frac{77}{1.1} = 70 \]

6. **Determine the Percentage by which CP is lower than MP:**
- Now we know:
- MP = 100
- CP = 70
- The difference between MP and CP is:
\[ MP - CP = 100 - 70 = 30 \]
- To find the percentage by which CP is lower than MP:
\[ \text{Percentage lower} = \left(\frac{MP - CP}{MP}\right) \times 100 = \left(\frac{30}{100}\right) \times 100 = 30\% \]

### Final Answer:
The Cost Price (CP) is lower than the Market Price (MP) by **30%**.

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