Renu sold an article at a loss of 8 percent. Had she bought it at 10% less and sold for Rs 36 more, she would have gained 20%. Find the cost price of the article.

Answer

To find the cost price of the article that Renu sold, we can follow these steps:

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be Rs 100 for simplicity in calculations.

### Step 2: Calculate Selling Price at a Loss of 8%
Since Renu sold the article at a loss of 8%, we can calculate the selling price (SP) as follows:
\[ SP = CP - (8\% \text{ of } CP) = 100 - (0.08 \times 100) = 100 - 8 = 92 \text{ Rs} \]

### Step 3: Calculate Cost Price at 10% Less
If Renu had bought the article at 10% less, the new cost price would be:
\[ New \, CP = CP - (10\% \text{ of } CP) = 100 - (0.10 \times 100) = 100 - 10 = 90 \text{ Rs} \]

### Step 4: Calculate Selling Price for a Gain of 20%
If she sold this article for Rs 36 more than the original selling price, the new selling price would be:
\[ New \, SP = 92 + 36 = 128 \text{ Rs} \]
To find the selling price that gives a gain of 20% on the new cost price:
\[ New \, SP = New \, CP + (20\% \text{ of } New \, CP) = 90 + (0.20 \times 90) = 90 + 18 = 108 \text{ Rs} \]

### Step 5: Set Up the Equation
We know that the new selling price (Rs 128) should equal the selling price calculated with a gain of 20% (Rs 108). Therefore, we can set up the equation:
\[ 128 - 92 = 36 \]
This means the difference in selling prices is Rs 36.

### Step 6: Calculate the Cost Price Based on the Difference
From the previous calculations, we found that a difference of Rs 16 in selling prices corresponds to a cost price of Rs 100. Therefore, we can find the cost price for a difference of Rs 36:
\[ \text{If } 16 \text{ Rs difference corresponds to } 100 \text{ Rs cost price, then for } 36 \text{ Rs difference:} \]
\[ \text{Cost Price} = \frac{100}{16} \times 36 = 225 \text{ Rs} \]

### Conclusion
Thus, the cost price of the article is Rs 225.

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