Anurag loses one-seventh of the cost by selling a pen for ₹ 144. If the pen is sold for ₹ 189, what is the gain percent?
(a)`11%`
(b)`12.5%`
(c)`11.5%`
(d)`14%`

Options

A. `11%`
B. `12.5%`
C. `11.5%`
D. `14%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Loss
Anurag loses one-seventh of the cost price (CP) when he sells the pen for ₹144. This means that if the cost price is represented as CP, then the loss can be expressed as:
\[ \text{Loss} = \frac{1}{7} \times \text{CP} \]

### Step 2: Relate Selling Price and Cost Price
Since he sells the pen for ₹144 and incurs a loss of one-seventh of the cost price, we can express the selling price (SP) in terms of CP:
\[ \text{SP} = \text{CP} - \text{Loss} \]
Substituting the loss:
\[ 144 = \text{CP} - \frac{1}{7} \text{CP} \]

### Step 3: Simplify the Equation
To simplify the equation, we can combine the terms on the right:
\[ 144 = \text{CP} \left(1 - \frac{1}{7}\right) \]
\[ 144 = \text{CP} \left(\frac{7}{7} - \frac{1}{7}\right) \]
\[ 144 = \text{CP} \left(\frac{6}{7}\right) \]

### Step 4: Solve for Cost Price
Now, we can solve for CP:
\[ \text{CP} = 144 \times \frac{7}{6} \]
\[ \text{CP} = 144 \times \frac{7}{6} = 144 \div 6 \times 7 = 24 \times 7 = 168 \]

### Step 5: Calculate Profit When Selling at ₹189
Now, if the pen is sold for ₹189, we can calculate the profit:
\[ \text{Profit} = \text{SP} - \text{CP} \]
\[ \text{Profit} = 189 - 168 = 21 \]

### Step 6: Calculate Gain Percentage
To find the gain percentage, we use the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left(\frac{21}{168}\right) \times 100 \]

### Step 7: Simplify the Gain Percentage Calculation
Now we can simplify:
\[ \text{Gain Percentage} = \left(\frac{21 \times 100}{168}\right) \]
\[ = \frac{2100}{168} \]

Now, simplifying \( \frac{2100}{168} \):
\[ 2100 \div 21 = 100 \]
\[ 168 \div 21 = 8 \]
Thus:
\[ \text{Gain Percentage} = \frac{100}{8} = 12.5\% \]

### Final Answer
The gain percentage when the pen is sold for ₹189 is **12.5%**.