By selling an umbrella for Rs. 336, a shopkeeper loses 4%. At what price must he sell it to gain 4%?

Answer

To solve the problem step by step, we will follow the process of calculating the cost price (CP) of the umbrella first and then determine the selling price (SP) required to achieve a 4% gain.

### Step 1: Identify the given values
- Selling Price (SP) = Rs. 336
- Loss Percentage = 4%

### Step 2: Calculate the Cost Price (CP)
To find the cost price when there is a loss, we use the formula:

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

Substituting the values we have:

\[ CP = \frac{100}{100 - 4} \times 336 \]

\[ CP = \frac{100}{96} \times 336 \]

### Step 3: Simplify the calculation
Now, we will calculate:

\[ CP = \frac{100 \times 336}{96} \]

Calculating the multiplication:

\[ CP = \frac{33600}{96} \]

Now, dividing:

\[ CP = 350 \]

So, the Cost Price (CP) of the umbrella is Rs. 350.

### Step 4: Calculate the Selling Price for a 4% Gain
Now that we have the cost price, we need to find the new selling price (SP) to achieve a 4% gain. We use the formula:

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

Substituting the values:

\[ SP = \left( \frac{100 + 4}{100} \right) \times 350 \]

\[ SP = \left( \frac{104}{100} \right) \times 350 \]

### Step 5: Simplify the calculation
Now, we will calculate:

\[ SP = 1.04 \times 350 \]

Calculating the multiplication:

\[ SP = 364 \]

So, the Selling Price (SP) to gain 4% is Rs. 364.

### Final Answer
The shopkeeper must sell the umbrella for Rs. 364 to gain 4%.

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