A company gives 10% discount on MP and earns 20% profit later on due to increase in CP by 10% and MP is increased by 40%. If discount % is same as before. Find new profit%.

Answer

To solve the problem step by step, we will first define the variables and then calculate the new profit percentage after the changes in cost price (CP) and mark price (MP).

### Step-by-Step Solution

1. **Define Initial Values:**
- Let the initial Mark Price (MP) be 100.
- The discount given is 10%, so the Selling Price (SP) can be calculated as:
\[ SP = MP - \text{Discount} = 100 - (10\% \text{ of } 100) = 100 - 10 = 90 \]

2. **Calculate Initial Cost Price (CP):**
- Given that there is a 20% profit, we can express this as:
\[ SP = CP + 20\% \text{ of } CP \]
This means:
\[ 90 = CP + 0.2 \times CP = 1.2 \times CP \]
Rearranging gives:
\[ CP = \frac{90}{1.2} = 75 \]

3. **Adjust Cost Price (CP) for Increase:**
- The CP is increased by 10%, so the new CP becomes:
\[ \text{New CP} = CP + 10\% \text{ of } CP = 75 + 0.1 \times 75 = 75 + 7.5 = 82.5 \]

4. **Adjust Mark Price (MP) for Increase:**
- The MP is increased by 40%, so the new MP becomes:
\[ \text{New MP} = MP + 40\% \text{ of } MP = 100 + 0.4 \times 100 = 100 + 40 = 140 \]

5. **Calculate New Selling Price (SP) After Discount:**
- The discount remains at 10%, so the new Selling Price is:
\[ \text{New SP} = \text{New MP} - \text{Discount} = 140 - (10\% \text{ of } 140) = 140 - 14 = 126 \]

6. **Calculate New Profit:**
- The profit can be calculated as:
\[ \text{Profit} = \text{New SP} - \text{New CP} = 126 - 82.5 = 43.5 \]

7. **Calculate New Profit Percentage:**
- The profit percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{New CP}}\right) \times 100 = \left(\frac{43.5}{82.5}\right) \times 100 \approx 52.73\% \]

### Final Answer
The new profit percentage is approximately **53%**.