A sold a watch at a gain of 5% to B and B sold it to C at a gain of 4%. If C paid Rs. 91 for it, the price paid by A is :

Options

A. Rs83.33
B. Rs84.33
C. Rs83
D. Rs82.81

Answer

To solve the problem step by step, we will follow the sequence of transactions between A, B, and C, and calculate the price paid by A for the watch.

### Step 1: Understand the Selling Prices
- A sells the watch to B at a gain of 5%.
- B sells the watch to C at a gain of 4%.
- C pays Rs. 91 for the watch.

### Step 2: Set Up the Initial Price
Let the price paid by A for the watch be \( P_A \). We can assume \( P_A = 100 \) units for simplicity in calculations.

### Step 3: Calculate the Selling Price from A to B
A sells the watch to B at a gain of 5%. Therefore, the selling price from A to B is calculated as follows:
\[ P_B = P_A + (5\% \text{ of } P_A) = 100 + \left(\frac{5}{100} \times 100\right) = 100 + 5 = 105 \text{ units} \]

### Step 4: Calculate the Selling Price from B to C
B sells the watch to C at a gain of 4%. Therefore, the selling price from B to C is calculated as follows:
\[ P_C = P_B + (4\% \text{ of } P_B) = 105 + \left(\frac{4}{100} \times 105\right) = 105 + 4.2 = 109.2 \text{ units} \]

### Step 5: Relate C's Payment to the Selling Price
We know that C paid Rs. 91 for the watch, which corresponds to the 109.2 units. Therefore, we can find the value of 1 unit:
\[ 1 \text{ unit} = \frac{91}{109.2} \]

### Step 6: Calculate the Price Paid by A
To find the price paid by A (which we assumed to be 100 units), we can set up the equation:
\[ P_A = 100 \times \left(\frac{91}{109.2}\right) \]

### Step 7: Simplify the Calculation
Now we can calculate:
\[ P_A = \frac{9100}{109.2} \]

### Step 8: Perform the Division
Calculating \( \frac{9100}{109.2} \):
\[ P_A \approx 83.33 \]

### Conclusion
The price paid by A for the watch is approximately Rs. 83.33.

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