By selling a table for Rs1140, a man loses 5%. In order to gain 5%, the table must be sold for

Options

A. 1260
B. 1320
C. 1180
D. 1250

Answer

To solve the problem step by step, we need to find the cost price (CP) of the table first and then determine the selling price (SP) required to achieve a 5% gain.

### Step 1: Determine the Cost Price (CP)
Let the cost price of the table be \( x \).

Since the man incurs a loss of 5%, the selling price (SP) can be expressed as:
\[ SP = CP - \text{Loss} \]
The loss is calculated as:
\[ \text{Loss} = \frac{5}{100} \times x = \frac{x}{20} \]
Thus, the selling price becomes:
\[ SP = x - \frac{x}{20} = \frac{20x - x}{20} = \frac{19x}{20} \]
According to the problem, the selling price is given as Rs 1140:
\[ \frac{19x}{20} = 1140 \]

### Step 2: Solve for CP (x)
To find \( x \), we can rearrange the equation:
\[ 19x = 1140 \times 20 \]
Calculating the right side:
\[ 19x = 22800 \]
Now, divide both sides by 19:
\[ x = \frac{22800}{19} = 1200 \]
So, the cost price (CP) of the table is Rs 1200.

### Step 3: Calculate Selling Price for 5% Gain
To find the selling price for a 5% gain, we calculate:
\[ \text{Selling Price for 5% gain} = CP + \text{Gain} \]
The gain is:
\[ \text{Gain} = \frac{5}{100} \times CP = \frac{5}{100} \times 1200 = 60 \]
Thus, the selling price for a 5% gain is:
\[ SP = 1200 + 60 = 1260 \]

### Final Answer
The table must be sold for Rs 1260 in order to gain 5%.

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