Manjeet singh sold an article for ₹9000 gaining 1/5 of its C.P. Find the gain %.

Options

A. 10%
B. 22%
C. 20%
D. 25%

Answer

To solve the problem, we need to find the gain percentage when Manjeet Singh sold an article for ₹9000, gaining 1/5 of its cost price (C.P.). Here’s a step-by-step solution:

### Step 1: Understand the Given Information
- Selling Price (SP) = ₹9000
- Gain = 1/5 of Cost Price (C.P.)

### Step 2: Set Up the Relationship
Let the Cost Price (C.P.) be denoted as \( x \). According to the problem, the gain is given by:
\[ \text{Gain} = \frac{1}{5} \times x \]

### Step 3: Express Selling Price in Terms of C.P.
The Selling Price (SP) can also be expressed in terms of C.P. and Gain:
\[ \text{SP} = \text{C.P.} + \text{Gain} \]
Substituting the values we have:
\[ 9000 = x + \frac{1}{5}x \]

### Step 4: Combine the Terms
To combine the terms on the right side, we can express \( x \) as \( \frac{5}{5}x \):
\[ 9000 = \frac{5}{5}x + \frac{1}{5}x = \frac{6}{5}x \]

### Step 5: Solve for C.P.
Now, we can solve for \( x \):
\[ 9000 = \frac{6}{5}x \]
Multiplying both sides by \( \frac{5}{6} \):
\[ x = 9000 \times \frac{5}{6} = 7500 \]
So, the Cost Price (C.P.) is ₹7500.

### Step 6: Calculate the Gain
Now that we have the C.P., we can calculate the Gain:
\[ \text{Gain} = \frac{1}{5} \times 7500 = 1500 \]

### Step 7: Calculate the Gain Percentage
The Gain Percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{C.P.}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{1500}{7500} \right) \times 100 = 20\% \]

### Conclusion
The gain percentage is 20%.

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