On selling a chair for Rs.680, a man loses 15%. To gain 15% it must be sold for

Options

A. Rs.800
B. Rs.860
C. Rs.920
D. Rs.884

Answer

To solve the problem step by step, we need to find the cost price of the chair first and then calculate the selling price needed to gain 15%.

### Step 1: Understand the loss percentage
The chair is sold for Rs. 680 at a loss of 15%. This means that the selling price is 85% of the cost price (100% - 15% = 85%).

### Step 2: Set up the equation
Let the cost price (CP) of the chair be denoted as \( x \). According to the information given:
\[ 0.85x = 680 \]

### Step 3: Solve for the cost price
To find \( x \), we can rearrange the equation:
\[ x = \frac{680}{0.85} \]

Now, calculate \( x \):
\[ x = \frac{680}{0.85} = 800 \]
So, the cost price of the chair is Rs. 800.

### Step 4: Calculate the selling price for a 15% gain
To find the selling price (SP) for a 15% gain, we need to calculate 15% of the cost price and add it to the cost price:
\[ \text{Gain} = 15\% \text{ of } 800 = \frac{15}{100} \times 800 = 120 \]
Now, add this gain to the cost price to find the selling price:
\[ \text{Selling Price} = CP + \text{Gain} = 800 + 120 = 920 \]

### Final Answer
To gain 15%, the chair must be sold for Rs. 920.

---