Meenakshi sells a pen for Rs.54 and loses `1/10` of her outlay. Find (i) the cost of the pen and (ii) the loss percent.

Answer

To solve the problem step by step, we will find both the cost price of the pen and the loss percent.

### Step 1: Understand the given information
- Selling Price (SP) = Rs. 54
- Loss = 1/10 of the Cost Price (CP)

### Step 2: Set up the equation for loss
Since the loss is given as 1/10 of the cost price, we can express this mathematically:
\[ \text{Loss} = \frac{1}{10} \times \text{CP} \]

### Step 3: Relate Selling Price, Cost Price, and Loss
The relationship between Selling Price, Cost Price, and Loss can be expressed as:
\[ \text{SP} = \text{CP} - \text{Loss} \]

Substituting the expression for Loss from Step 2 into this equation:
\[ 54 = \text{CP} - \frac{1}{10} \times \text{CP} \]

### Step 4: Simplify the equation
We can rewrite the equation:
\[ 54 = \text{CP} - \frac{1}{10} \text{CP} \]
\[ 54 = \frac{10}{10} \text{CP} - \frac{1}{10} \text{CP} \]
\[ 54 = \frac{9}{10} \text{CP} \]

### Step 5: Solve for Cost Price (CP)
To find CP, we can rearrange the equation:
\[ \text{CP} = 54 \times \frac{10}{9} \]
\[ \text{CP} = 60 \]

### Step 6: Calculate the Loss
Now that we have the Cost Price, we can calculate the Loss:
\[ \text{Loss} = \frac{1}{10} \times \text{CP} = \frac{1}{10} \times 60 = 6 \]

### Step 7: Calculate the Loss Percent
Loss percent can be calculated using the formula:
\[ \text{Loss Percent} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percent} = \left( \frac{6}{60} \right) \times 100 = 10\% \]

### Final Answers:
(i) The cost of the pen (CP) = Rs. 60
(ii) The loss percent = 10%

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