'w' purchased Mobile and spent 110 to repair it. Then he sold it to 'x' at a profit of 20%. 'x' sold it to 'y'at a loss of 10%. 'y' sold it to 'z' at a profit of 10% for Rs 1188. Find the price at which 'w' purchased the Mobile.

Options

A. Rs 890
B. Rs 870
C. Rs 888
D. Rs 880

Answer

To find the price at which 'W' purchased the mobile, we can follow these steps:

### Step 1: Understand the Selling Price of 'Y' to 'Z'
'Y' sold the mobile to 'Z' at a profit of 10% for Rs 1188. This means that Rs 1188 represents 110% of the cost price for 'Y'.

**Calculation:**
Let the cost price of 'Y' be \( CP_Y \).
\[ CP_Y \times 1.10 = 1188 \]
\[ CP_Y = \frac{1188}{1.10} = 1080 \]

### Step 2: Determine the Selling Price of 'X' to 'Y'
'X' sold the mobile to 'Y' at a loss of 10%. Therefore, the cost price for 'X' can be calculated as follows:

**Calculation:**
Let the cost price of 'X' be \( CP_X \).
\[ CP_Y \times 0.90 = 1080 \]
\[ CP_X = \frac{1080}{0.90} = 1200 \]

### Step 3: Find the Selling Price of 'W' to 'X'
'W' sold the mobile to 'X' at a profit of 20%. Thus, we can find the cost price for 'W'.

**Calculation:**
Let the cost price of 'W' be \( CP_W \).
\[ CP_X \times 1.20 = 1200 \]
\[ CP_W = \frac{1200}{1.20} = 1000 \]

### Step 4: Account for the Repair Cost
'W' spent Rs 110 on repairs. Therefore, the purchase price of the mobile for 'W' can be calculated as follows:

**Calculation:**
\[ \text{Price at which 'W' purchased the mobile} = CP_W - \text{Repair Cost} \]
\[ \text{Price} = 1000 - 110 = 890 \]

### Final Answer
The price at which 'W' purchased the mobile is **Rs 890**.

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