By selling an article for Rs 110, a man loses `12%`. For how much should he sell it to gain `8%` ?

Options

A. A)Rs 145
B. B)Rs 120
C. C)Rs 135
D. D)Rs 130

Answer

To solve the problem step by step, we need to determine the cost price (CP) of the article first and then find the selling price (SP) required to achieve an 8% gain.

### Step 1: Determine the Cost Price (CP)
Given that the selling price (SP) is Rs 110 and the man incurs a loss of 12%, we can set up the following relationship:

Loss % = (CP - SP) / CP × 100

Here, we know:
- SP = Rs 110
- Loss % = 12%

From the loss percentage formula, we can rearrange it to find the cost price (CP):

12 = (CP - 110) / CP × 100

### Step 2: Solve for CP
Rearranging the equation gives us:

0.12 = (CP - 110) / CP

Multiplying both sides by CP:

0.12 * CP = CP - 110

Now, rearranging gives:

CP - 0.12 * CP = 110

0.88 * CP = 110

Now, divide both sides by 0.88:

CP = 110 / 0.88

Calculating this gives:

CP = 125

### Step 3: Calculate the Selling Price for 8% Gain
Now that we have the cost price, we can calculate the selling price required for an 8% gain.

Gain % = (SP - CP) / CP × 100

We know:
- Gain % = 8%
- CP = 125

Using the gain percentage formula:

8 = (SP - 125) / 125 × 100

### Step 4: Solve for SP
Rearranging gives us:

0.08 = (SP - 125) / 125

Multiplying both sides by 125:

0.08 * 125 = SP - 125

Now, calculate 0.08 * 125:

SP - 125 = 10

Adding 125 to both sides gives:

SP = 135

### Final Answer
The selling price to gain 8% is Rs 135.

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