A shopkeeper sells a sari for Rs 266 after giving discount of 5% . If he had not given the discount then he would gain 12 % profit of C.P. Find C.P. of each sari.

Answer

To find the cost price (C.P.) of the sari, we can follow these steps:

### Step 1: Determine the Selling Price (S.P.) after Discount
The selling price of the sari after a 5% discount is given as Rs. 266.

### Step 2: Calculate the Marked Price (M.P.)
Let the marked price (M.P.) be \( x \). Since a discount of 5% is given, we can express the selling price as:
\[ S.P. = M.P. - \text{Discount} \]
The discount can be calculated as:
\[ \text{Discount} = 5\% \text{ of } M.P. = \frac{5}{100} \times x = \frac{x}{20} \]
Thus, we can write:
\[ 266 = x - \frac{x}{20} \]
To simplify this, we can express \( x \) in terms of a common denominator:
\[ 266 = \frac{20x - x}{20} = \frac{19x}{20} \]
Now, multiplying both sides by 20 to eliminate the fraction:
\[ 5320 = 19x \]
Now, divide both sides by 19 to find \( x \):
\[ x = \frac{5320}{19} = 280 \]
So, the marked price (M.P.) is Rs. 280.

### Step 3: Calculate the Cost Price (C.P.)
We know that if no discount is given, the shopkeeper makes a profit of 12%. This means:
\[ S.P. = C.P. + \text{Profit} \]
The profit can be expressed as:
\[ \text{Profit} = 12\% \text{ of } C.P. = \frac{12}{100} \times C.P. = \frac{3}{25} \times C.P. \]
Thus, we can write:
\[ S.P. = C.P. + \frac{3}{25} \times C.P. = C.P. \left(1 + \frac{3}{25}\right) = C.P. \left(\frac{28}{25}\right) \]
Since the selling price without discount is equal to the marked price:
\[ 280 = C.P. \left(\frac{28}{25}\right) \]
To find the cost price, we can rearrange this equation:
\[ C.P. = 280 \times \frac{25}{28} \]
Calculating this gives:
\[ C.P. = 250 \]

### Final Answer
The cost price (C.P.) of each sari is Rs. 250.

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