X sells shoes to Y at a profit of 20% and Y sells same shoes to Z at a profit of 23%. If Z pays Rs. 3321 for the shoes, then what was the cost price (in Rs.) of shoes for X?

Options

A. 1950
B. 2450
C. 2250
D. 2045

Answer

To find the cost price of the shoes for X, we will follow these steps:

### Step 1: Understand the Selling Price from Z to Y
Z pays Rs. 3321 for the shoes. This is the selling price for Y when he sold the shoes to Z.

### Step 2: Calculate the Cost Price for Y
Y sells the shoes to Z at a profit of 23%. Therefore, if we let the cost price for Y be \( CP_Y \), then the selling price (SP_Y) can be expressed as:
\[ SP_Y = CP_Y + 0.23 \times CP_Y = 1.23 \times CP_Y \]
Since we know that \( SP_Y = 3321 \):
\[ 1.23 \times CP_Y = 3321 \]
Now, we can solve for \( CP_Y \):
\[ CP_Y = \frac{3321}{1.23} \]

### Step 3: Calculate \( CP_Y \)
Calculating \( CP_Y \):
\[ CP_Y = \frac{3321}{1.23} \approx 2700 \]

### Step 4: Calculate the Cost Price for X
X sells the shoes to Y at a profit of 20%. Therefore, if we let the cost price for X be \( CP_X \), then the selling price (SP_X) can be expressed as:
\[ SP_X = CP_X + 0.20 \times CP_X = 1.20 \times CP_X \]
Since we know that \( SP_X = CP_Y \):
\[ 1.20 \times CP_X = 2700 \]
Now, we can solve for \( CP_X \):
\[ CP_X = \frac{2700}{1.20} \]

### Step 5: Calculate \( CP_X \)
Calculating \( CP_X \):
\[ CP_X = \frac{2700}{1.20} = 2250 \]

### Final Answer
Thus, the cost price of the shoes for X is Rs. 2250.

---