Subhash purchased a tape recorder at `(9)/(10)` th of its selling price and sold it at 8% more than its selling price. His gain is:

Answer

To find Subhash's gain percentage from the purchase and sale of the tape recorder, we will follow these steps:

### Step 1: Define the Selling Price (SP)
Let's assume the selling price (SP) of the tape recorder is \( x \).

### Step 2: Calculate the Cost Price (CP)
According to the problem, Subhash purchased the tape recorder at \( \frac{9}{10} \) of its selling price. Therefore, the cost price (CP) can be calculated as:
\[ CP = \frac{9}{10} \times SP = \frac{9}{10} \times x \]

### Step 3: Calculate the Selling Price after the Increase
Subhash sold the tape recorder at 8% more than its selling price. Thus, the selling price after the increase can be calculated as:
\[ \text{New SP} = SP + 8\% \text{ of } SP = SP + \frac{8}{100} \times SP = SP \times \left(1 + \frac{8}{100}\right) = SP \times \frac{108}{100} \]
Substituting \( SP = x \):
\[ \text{New SP} = x \times \frac{108}{100} = 1.08x \]

### Step 4: Calculate the Profit
Now, we can calculate the profit made by Subhash:
\[ \text{Profit} = \text{New SP} - CP = 1.08x - \frac{9}{10}x \]
To simplify this, we need a common denominator:
\[ \frac{9}{10}x = 0.9x \]
Thus,
\[ \text{Profit} = 1.08x - 0.9x = 0.18x \]

### Step 5: Calculate the Gain Percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left(\frac{0.18x}{0.9x}\right) \times 100 \]
The \( x \) cancels out:
\[ \text{Gain Percentage} = \left(\frac{0.18}{0.9}\right) \times 100 = 0.2 \times 100 = 20\% \]

### Final Answer
Subhash's gain percentage is **20%**.

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