Mc-n- Roe, a popular garment store in New York, purchased some pieces of garments each at the same cost price. The store then sold each garment at 20% profit . Had the store charged $10 more for each garment, it would have made 25% profit on its cost. What was the cost of each piece of garment that the store procured ?

Options

A. 200
B. 240
C. 250
D. 300

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information provided in the question.

### Step 1: Define Variables
Let:
- \( CP \) = Cost Price of each garment
- \( SP_1 \) = Selling Price at 20% profit
- \( SP_2 \) = Selling Price at 25% profit

### Step 2: Write the Selling Price at 20% Profit
The selling price at 20% profit can be expressed as:
\[ SP_1 = CP + 0.20 \times CP = CP \times (1 + 0.20) = 1.20 \times CP \]

### Step 3: Write the Selling Price at 25% Profit
The selling price at 25% profit can be expressed as:
\[ SP_2 = CP + 0.25 \times CP = CP \times (1 + 0.25) = 1.25 \times CP \]

### Step 4: Relate the Selling Prices
According to the problem, if the store had charged $10 more than the selling price at 20% profit, it would have made a 25% profit. Therefore, we can write:
\[ SP_2 = SP_1 + 10 \]

### Step 5: Substitute the Selling Prices
Substituting the expressions for \( SP_1 \) and \( SP_2 \) into the equation gives:
\[ 1.25 \times CP = 1.20 \times CP + 10 \]

### Step 6: Simplify the Equation
Now, we can simplify the equation:
\[ 1.25 \times CP - 1.20 \times CP = 10 \]
\[ 0.05 \times CP = 10 \]

### Step 7: Solve for Cost Price
To find \( CP \), we divide both sides by 0.05:
\[ CP = \frac{10}{0.05} = 200 \]

### Conclusion
The cost of each piece of garment that the store procured is:
\[ \boxed{200} \]