A company offers 20% discount and earns profit of 25% . Further it increases production cost by 10% and issues new price list which is 25% more than the previous one . If company offers same discount as earlier then what will be its profit % at increased production cost.

Answer

To solve the problem step by step, we will follow the given information and calculate the required values.

### Step 1: Determine the Selling Price (SP) from the given Profit Percentage
We know that the company earns a profit of 25%. This means that the Selling Price (SP) is 125% of the Cost Price (CP).

Let the Cost Price (CP) be \( x \).

\[ SP = 125\% \text{ of } CP = \frac{125}{100} \times x = 1.25x \]

### Step 2: Determine the Selling Price (SP) from the given Discount Percentage
The company offers a discount of 20% on the Market Price (MP). This means that the Selling Price (SP) can also be expressed as:

\[ SP = MP - \text{Discount} \]

If we assume the Market Price (MP) is \( 100 \) (for simplicity), then the discount is:

\[ \text{Discount} = 20\% \text{ of } MP = \frac{20}{100} \times 100 = 20 \]

Thus, the Selling Price (SP) becomes:

\[ SP = 100 - 20 = 80 \]

### Step 3: Set the two expressions for SP equal to each other
From Step 1 and Step 2, we have:

\[ 1.25x = 80 \]

### Step 4: Solve for CP
Now, we can solve for \( x \):

\[ x = \frac{80}{1.25} = 64 \]

So, the original Cost Price (CP) is \( 64 \).

### Step 5: Calculate the new Cost Price (CP) after a 10% increase
The production cost increases by 10%. Therefore, the new Cost Price (CP) is:

\[ \text{New CP} = CP + 10\% \text{ of } CP = 64 + 0.10 \times 64 = 64 + 6.4 = 70.4 \]

### Step 6: Calculate the new Market Price (MP) after a 25% increase
The Market Price (MP) is increased by 25%. Therefore, the new Market Price (MP) is:

\[ \text{New MP} = MP + 25\% \text{ of } MP = 100 + 0.25 \times 100 = 100 + 25 = 125 \]

### Step 7: Calculate the new Selling Price (SP) after applying the same discount
The company offers the same discount of 20% on the new Market Price (MP):

\[ \text{Discount} = 20\% \text{ of } 125 = \frac{20}{100} \times 125 = 25 \]

Thus, the new Selling Price (SP) becomes:

\[ \text{New SP} = \text{New MP} - \text{Discount} = 125 - 25 = 100 \]

### Step 8: Calculate the new Profit
Now, we can find the profit by subtracting the new Cost Price (CP) from the new Selling Price (SP):

\[ \text{Profit} = \text{New SP} - \text{New CP} = 100 - 70.4 = 29.6 \]

### Step 9: Calculate the Profit Percentage
Finally, we calculate the profit percentage:

\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{New CP}} \right) \times 100 = \left( \frac{29.6}{70.4} \right) \times 100 \approx 42.0\% \]

### Final Answer
The profit percentage at the increased production cost is approximately **42.0%**.

---