To solve the problem step by step, we will follow the process of applying successive discounts and then calculating the selling price based on a single discount.
### Step 1: Understand the Marked Price and Discounts
The marked price (MP) of the commodity is Rs. 10,000. The successive discounts given are:
- First discount: 10%
- Second discount: 20%
- Third discount: k%
The final selling price (SP) after these discounts is Rs. 6,120.
### Step 2: Apply the First Discount
Calculate the first discount of 10% on the marked price:
\[
\text{First Discount} = 10\% \text{ of } 10,000 = \frac{10}{100} \times 10,000 = 1,000
\]
Now, subtract this discount from the marked price:
\[
\text{Price after First Discount} = 10,000 - 1,000 = 9,000
\]
### Step 3: Apply the Second Discount
Now apply the second discount of 20% on the new price (Rs. 9,000):
\[
\text{Second Discount} = 20\% \text{ of } 9,000 = \frac{20}{100} \times 9,000 = 1,800
\]
Subtract this discount from the price after the first discount:
\[
\text{Price after Second Discount} = 9,000 - 1,800 = 7,200
\]
### Step 4: Apply the Third Discount
Let’s denote the third discount (k%) on the price after the second discount (Rs. 7,200). The selling price after all three discounts is given as Rs. 6,120:
\[
\text{Selling Price} = 7,200 - \left(\frac{k}{100} \times 7,200\right) = 6,120
\]
This can be rearranged to find k:
\[
7,200 - 6,120 = \frac{k}{100} \times 7,200
\]
Calculating the left side:
\[
1,080 = \frac{k}{100} \times 7,200
\]
Now, solve for k:
\[
k = \frac{1,080 \times 100}{7,200} = 15
\]
### Step 5: Calculate the Selling Price with a Single Discount
The problem states that if the shopkeeper gives a single discount of (k + 20)%. Since we found k = 15, the new discount is:
\[
k + 20 = 15 + 20 = 35\%
\]
Now, calculate the selling price with this single discount:
\[
\text{Single Discount} = 35\% \text{ of } 10,000 = \frac{35}{100} \times 10,000 = 3,500
\]
Subtract this discount from the marked price:
\[
\text{Selling Price} = 10,000 - 3,500 = 6,500
\]
### Final Answer
The selling price of the commodity when a single discount of (k + 20)% is applied is Rs. 6,500.
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