By selling an article for Rs 77 a person gained `(1)/(10)` of his outlay. What would he have gained orlost percent by selling it for Rs 63?

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the article based on the information provided and then calculate the loss percentage when the article is sold for Rs 63.

### Step 1: Determine the Selling Price (SP) and Gain
The selling price (SP) of the article is given as Rs 77. The gain is stated to be \( \frac{1}{10} \) of the outlay (cost price).

### Step 2: Relate Gain to Cost Price
If we denote the cost price (CP) as \( x \), then the gain can be expressed as:
\[ \text{Gain} = \frac{1}{10} \times x \]
According to the relationship between selling price, cost price, and gain:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Substituting the values we have:
\[ 77 = x + \frac{1}{10}x \]
This can be simplified to:
\[ 77 = x + 0.1x = 1.1x \]

### Step 3: Solve for Cost Price (CP)
Now, we can solve for \( x \):
\[ x = \frac{77}{1.1} \]
Calculating this gives:
\[ x = 70 \]
Thus, the cost price (CP) of the article is Rs 70.

### Step 4: Calculate Loss when Selling Price is Rs 63
Now, we need to find out what happens when the article is sold for Rs 63. We will calculate the loss:
\[ \text{Loss} = \text{CP} - \text{SP} = 70 - 63 = 7 \]

### Step 5: Calculate Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{7}{70} \right) \times 100 \]
Calculating this gives:
\[ \text{Loss Percentage} = 10\% \]

### Final Answer
If the article is sold for Rs 63, the person would incur a loss of 10%.

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