On selling a jug for ₹ 144, a man loses`1/7` of his outlay. If it is sold for ₹ 189, what is the gain%?

Options

A. `12.5%`
B. `25%`
C. `30%`
D. `50%`

Answer

To solve the problem step by step, we will first determine the cost price of the jug and then calculate the gain percentage when it is sold for ₹189.

### Step 1: Define the Cost Price
Let the cost price (CP) of the jug be denoted as \( X \).

### Step 2: Calculate the Loss
According to the problem, when the jug is sold for ₹144, the man incurs a loss of \( \frac{1}{7} \) of his cost price. Therefore, the loss can be expressed as:
\[ \text{Loss} = \frac{1}{7} \times X \]

### Step 3: Relate Selling Price and Cost Price
The selling price (SP) when sold at a loss is given by:
\[ \text{SP} = \text{CP} - \text{Loss} \]
Substituting the values we have:
\[ 144 = X - \frac{1}{7}X \]

### Step 4: Simplify the Equation
To simplify the equation, we can express \( X - \frac{1}{7}X \) as:
\[ X - \frac{1}{7}X = \frac{7}{7}X - \frac{1}{7}X = \frac{6}{7}X \]
Thus, we have:
\[ 144 = \frac{6}{7}X \]

### Step 5: Solve for Cost Price
Now, we can solve for \( X \):
\[ X = 144 \times \frac{7}{6} \]
Calculating this gives:
\[ X = 144 \times \frac{7}{6} = 144 \times 1.1667 = 168 \]
So, the cost price \( X \) is ₹168.

### Step 6: Calculate Gain When Sold for ₹189
Now, we need to find the gain when the jug is sold for ₹189. The gain can be calculated as:
\[ \text{Gain} = \text{SP} - \text{CP} = 189 - 168 = 21 \]

### Step 7: Calculate Gain Percentage
The gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{21}{168} \right) \times 100 \]
Calculating this gives:
\[ \text{Gain Percentage} = 0.125 \times 100 = 12.5\% \]

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