A sold a watch to Bat 40% gain and B sold it to C at a loss of 20%.If C bought the watch for Rs 432 ,at what price did A purchase it?

Options

A. Rs 385
B. Rs 216
C. Rs 250
D. Rs550

Answer

To solve the problem step by step, we will follow the given information and calculations:

### Step 1: Understand the Problem
A sold a watch to B at a 40% gain, and B sold it to C at a 20% loss. C bought the watch for Rs 432. We need to find out the price at which A purchased the watch.

### Step 2: Define Variables
Let the cost price of the watch for A be \( x \).

### Step 3: Calculate Selling Price of A
Since A sold the watch at a 40% gain, the selling price (SP) of A can be calculated as:
\[ SP_A = x + 0.4x = 1.4x \]

### Step 4: Calculate Selling Price of B
B sold the watch to C at a 20% loss. Therefore, the selling price of B can be calculated as:
\[ SP_B = SP_A - 0.2 \times SP_A = 0.8 \times SP_A = 0.8 \times 1.4x = 1.12x \]

### Step 5: Set Up the Equation
We know that C bought the watch for Rs 432, which means:
\[ SP_B = 432 \]
Thus, we can set up the equation:
\[ 1.12x = 432 \]

### Step 6: Solve for x
To find the cost price of A, we will solve for \( x \):
\[ x = \frac{432}{1.12} \]

### Step 7: Perform the Division
Calculating \( \frac{432}{1.12} \):
\[ x = \frac{432 \times 100}{112} = \frac{43200}{112} \]
Now, simplifying \( \frac{43200}{112} \):
\[ 43200 \div 112 = 385.7142857 \approx 385.71 \]

### Step 8: Round to Nearest Whole Number
Since we are dealing with currency, we round this to the nearest whole number:
\[ x \approx 386 \]

### Final Answer
Thus, the price at which A purchased the watch is approximately Rs 386.

---