An electrician sells a room heater for ₹3220, gaining`1/6` of its cost price. Find his gain per cent

Answer

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

### Step 1: Understand the Given Information
The selling price (SP) of the room heater is ₹3220, and the gain is \( \frac{1}{6} \) of the cost price (CP).

### Step 2: Set Up the Equation
Let the cost price (CP) be \( x \). According to the problem, the gain can be expressed as:
\[ \text{Gain} = \frac{1}{6} \times x \]

### Step 3: Express Selling Price in Terms of Cost Price
The selling price can also be expressed in terms of the cost price and gain:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Substituting the values we have:
\[ 3220 = x + \frac{1}{6}x \]

### Step 4: Combine Like Terms
To combine the terms on the right side, we can express \( x \) as \( \frac{6}{6}x \):
\[ 3220 = \frac{6}{6}x + \frac{1}{6}x \]
\[ 3220 = \frac{7}{6}x \]

### Step 5: Solve for Cost Price
To find \( x \), we will multiply both sides by \( \frac{6}{7} \):
\[ x = 3220 \times \frac{6}{7} \]

### Step 6: Calculate the Cost Price
Now we will perform the calculation:
\[ x = 3220 \times \frac{6}{7} = 3220 \times 0.8571 \approx 2742.86 \]
So, the cost price (CP) is approximately ₹2742.86.

### Step 7: Calculate the Gain
Now we can calculate the gain:
\[ \text{Gain} = \frac{1}{6} \times 2742.86 \approx 457.14 \]

### Step 8: Calculate Gain Percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left(\frac{457.14}{2742.86}\right) \times 100 \approx 16.66\% \]

### Final Answer
The gain percentage is approximately **16.66%**.

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