By selling 90 pens for Rs. 80 a man loses 20%. What should be the selling price (in Rs.) of 90 pens for 20% profit?

Options

A. 90
B. 100
C. 110
D. 120

Answer

To solve the problem step by step, we will follow the explanation given in the video transcript.

### Step 1: Understand the Given Information
We know that:
- Selling Price (SP) of 90 pens = Rs. 80
- Loss Percentage = 20%

### Step 2: Calculate the Cost Price (CP)
To find the Cost Price (CP), we can use the formula for calculating CP when we know the SP and the loss percentage:

\[ CP = \frac{SP \times 100}{100 - \text{Loss Percentage}} \]

Substituting the values we have:

\[ CP = \frac{80 \times 100}{100 - 20} \]

### Step 3: Simplify the Calculation
Now, let's simplify the equation:

\[ CP = \frac{8000}{80} = 100 \]

So, the Cost Price (CP) of 90 pens is Rs. 100.

### Step 4: Calculate the Selling Price for 20% Profit
Now, we need to find the Selling Price (SP) for a profit of 20%. We can use the formula for SP when we know the CP and the profit percentage:

\[ SP = CP \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]

Substituting the values we have:

\[ SP = 100 \times \left(1 + \frac{20}{100}\right) \]

### Step 5: Simplify the Selling Price Calculation
Now, let's simplify the equation:

\[ SP = 100 \times \left(1 + 0.2\right) = 100 \times 1.2 = 120 \]

Thus, the Selling Price (SP) of 90 pens for a 20% profit is Rs. 120.

### Final Answer
The selling price of 90 pens for a 20% profit is **Rs. 120**.

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