An article was sold at a profit of 12%. If the cost price would be 10% less and selling price would be 5.75 more, there would be profit of 30%. Then at what price it should be sold to make a profit of 20%?

Options

A. 115
B. 120
C. 138
D. 215

Answer

To solve the problem step by step, we will break down the information given and use it to find the required selling price for a 20% profit.

### Step 1: Define Variables
Let the original cost price (CP) of the article be \( CP \).

### Step 2: Calculate Selling Price with 12% Profit
If the article is sold at a profit of 12%, the selling price (SP) can be calculated as:
\[ SP = CP + 0.12 \times CP = 1.12 \times CP \]

### Step 3: Adjust Cost Price and Selling Price
According to the problem, if the cost price is 10% less, the new cost price becomes:
\[ CP' = CP - 0.10 \times CP = 0.90 \times CP \]
It is also given that the selling price would be increased by 5.75, so the new selling price becomes:
\[ SP' = SP + 5.75 = 1.12 \times CP + 5.75 \]

### Step 4: Calculate New Selling Price for 30% Profit
With the new cost price and selling price, the profit is 30%. Therefore, we can express this as:
\[ SP' = CP' + 0.30 \times CP' = 1.30 \times CP' \]
Substituting \( CP' \):
\[ SP' = 1.30 \times (0.90 \times CP) = 1.17 \times CP \]

### Step 5: Set Up the Equation
Now we have two expressions for \( SP' \):
1. \( SP' = 1.12 \times CP + 5.75 \)
2. \( SP' = 1.17 \times CP \)

Setting these equal gives us:
\[ 1.12 \times CP + 5.75 = 1.17 \times CP \]

### Step 6: Solve for CP
Rearranging the equation:
\[ 5.75 = 1.17 \times CP - 1.12 \times CP \]
\[ 5.75 = 0.05 \times CP \]
Now, solving for \( CP \):
\[ CP = \frac{5.75}{0.05} = 115 \]

### Step 7: Calculate Selling Price for 20% Profit
To find the selling price for a 20% profit, we calculate:
\[ SP_{20\%} = CP + 0.20 \times CP = 1.20 \times CP \]
Substituting \( CP = 115 \):
\[ SP_{20\%} = 1.20 \times 115 = 138 \]

### Final Answer
The selling price to make a profit of 20% should be **138**.

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