A person sold an article for Rs 136 and got 15% loss. Had he sold it for Rs x,he would have got a profit of 15%. Which one of the following is correct?

Options

A. `190 lt x lt 200`
B. `180 lt x lt 190`
C. `170 lt x lt 180`
D. `160 lt x lt 170`

Answer

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

### Step 1: Understand the given information
- Selling Price (SP1) = Rs 136
- Loss = 15%
- Selling Price (SP2) = Rs x
- Profit = 15%

### Step 2: Calculate the Cost Price (CP)
Since there is a loss of 15%, we can express the relationship between SP1 and CP as follows:
\[ SP1 = CP \times \left(1 - \frac{Loss}{100}\right) \]
Substituting the values:
\[ 136 = CP \times \left(1 - \frac{15}{100}\right) \]
\[ 136 = CP \times \left(\frac{85}{100}\right) \]
To find CP, we rearrange the equation:
\[ CP = \frac{136 \times 100}{85} \]

### Step 3: Simplify the Cost Price Calculation
Calculating CP:
\[ CP = \frac{13600}{85} \]
Dividing 13600 by 85:
\[ CP = 160 \]

### Step 4: Calculate the Selling Price for Profit
Now, we need to find SP2 (which is Rs x) when there is a profit of 15%. The relationship can be expressed as:
\[ SP2 = CP \times \left(1 + \frac{Profit}{100}\right) \]
Substituting the values:
\[ SP2 = 160 \times \left(1 + \frac{15}{100}\right) \]
\[ SP2 = 160 \times \left(\frac{115}{100}\right) \]

### Step 5: Simplify the Selling Price Calculation
Calculating SP2:
\[ SP2 = 160 \times 1.15 = 184 \]

### Step 6: Conclusion
Thus, the value of x (SP2) is Rs 184.

### Step 7: Determine the correct option
Now, we need to check which option includes the value 184. The options given are:
- Option A: 190
- Option B: 180
- Option C: 200

Since 184 lies between 180 and 190, the correct option is **Option B**.