A man sold an article at a loss of 10%. If he sells the article for Rs. 10 more he would have gained 5%. The cost price of the article is

Options

A. (a) Rs. 30
B. (b) Rs. 36.50
C. (c) Rs. 54.76
D. (d) Rs. 66.66

Answer

To solve the problem step by step, let's denote the cost price of the article as \( CP \).

### Step 1: Understand the Selling Price at Loss
When the man sells the article at a loss of 10%, the selling price (SP) can be expressed as:
\[ SP = CP - (10\% \text{ of } CP) = CP - 0.1 \times CP = 0.9 \times CP \]

### Step 2: Understand the Selling Price at Profit
If he sells the article for Rs. 10 more, he would have gained 5%. The new selling price can be expressed as:
\[ SP_{new} = CP + (5\% \text{ of } CP) = CP + 0.05 \times CP = 1.05 \times CP \]

### Step 3: Set Up the Equation
According to the problem, the new selling price is Rs. 10 more than the original selling price:
\[ SP_{new} = SP + 10 \]
Substituting the expressions for \( SP \) and \( SP_{new} \):
\[ 1.05 \times CP = 0.9 \times CP + 10 \]

### Step 4: Solve for CP
Now, we can solve for \( CP \):
\[ 1.05 \times CP - 0.9 \times CP = 10 \]
\[ 0.15 \times CP = 10 \]
\[ CP = \frac{10}{0.15} = \frac{10 \times 100}{15} = \frac{1000}{15} = \frac{200}{3} \approx 66.67 \]

### Conclusion
The cost price of the article is approximately Rs. 66.67.

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