A goldsmith has 361 rings of good. He sells some of them at a loss of 4% and rest at a profit of 15% making overal profit of 8%. Find the no. of rings sold at a profit of 15%/

Options

A. 171
B. 133
C. 218
D. 228

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the problem
The goldsmith has a total of 361 rings. He sells some at a loss of 4% and the rest at a profit of 15%. The overall profit he makes is 8%. We need to find out how many rings he sold at a profit of 15%.

### Step 2: Set up the profit/loss percentages
- Loss on some rings = 4%
- Profit on some rings = 15%
- Overall profit = 8%

### Step 3: Use the allegation method
We can use the allegation method to find the ratio of the rings sold at a loss to the rings sold at a profit.

- The difference between the profit percentage and the overall profit percentage:
\[ 15\% - 8\% = 7\% \]

- The difference between the overall profit percentage and the loss percentage:
\[ 8\% - (-4\%) = 8\% + 4\% = 12\% \]

### Step 4: Set up the ratio
Using the differences calculated:
- The ratio of rings sold at a loss to rings sold at a profit is:
\[ 7 : 12 \]

### Step 5: Calculate the total parts
The total parts in the ratio is:
\[ 7 + 12 = 19 \]

### Step 6: Calculate the value of one part
Since the total number of rings is 361, we can find the value of one part:
\[ \text{Value of one part} = \frac{361}{19} = 19 \]

### Step 7: Calculate the number of rings sold at a profit
The number of rings sold at a profit (which corresponds to 12 parts) is:
\[ \text{Number of rings sold at profit} = 12 \times 19 = 228 \]

### Conclusion
The number of rings sold at a profit of 15% is **228 rings**.

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