By selling an article for र720, a man loses 10%. At what price should he sell it to gain 5%?

Options

A. र 840
B. र 890
C. र 1000
D. र 995

Answer

To solve the problem step by step, we will follow the given information and perform calculations accordingly.

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

### Step 2: Calculate the Selling Price (SP) with Loss
According to the question, the man sells the article for \( ₹720 \) and incurs a loss of \( 10\% \).
The formula for selling price when there is a loss is:
\[ SP = CP - \text{Loss} \]
Since the loss is \( 10\% \) of the cost price, we can express it as:
\[ \text{Loss} = 0.1X \]
Thus, the selling price can be rewritten as:
\[ SP = X - 0.1X = 0.9X \]
Given that the selling price is \( ₹720 \), we can set up the equation:
\[ 0.9X = 720 \]

### Step 3: Solve for Cost Price (CP)
To find \( X \), we rearrange the equation:
\[ X = \frac{720}{0.9} \]
Calculating this gives:
\[ X = 800 \]
So, the cost price of the article is \( ₹800 \).

### Step 4: Calculate the Gain for Selling Price with Profit
Now, we need to find the selling price at which the man gains \( 5\% \).
The gain can be calculated as:
\[ \text{Gain} = 5\% \text{ of } CP = \frac{5}{100} \times 800 = 40 \]

### Step 5: Calculate the New Selling Price (SP)
The new selling price when there is a gain is given by:
\[ SP = CP + \text{Gain} \]
Substituting the values we have:
\[ SP = 800 + 40 = 840 \]

### Final Answer
The selling price to gain \( 5\% \) is \( ₹840 \).

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