A man earns a profit of 30% by selling an article for Rs. 169. To earn a profit of 40%, by how much per cent should he increase his selling price?

Options

A. a) 8.33
B. b) 7.69
C. c) 12.5
D. d) 9.09

Answer

To solve the problem step by step, we need to find out the cost price (CP) of the article first, then determine the new selling price (SP) for a 40% profit, and finally calculate the percentage increase in the selling price.

### Step 1: Find the Cost Price (CP)
Given that the selling price (SP) is Rs. 169 and the profit percentage is 30%, we can use the formula for selling price:

\[ SP = CP + (Profit\% \times CP) \]

This can be rewritten as:

\[ SP = CP \times \left(1 + \frac{Profit\%}{100}\right) \]

Substituting the values:

\[ 169 = CP \times \left(1 + \frac{30}{100}\right) \]

\[ 169 = CP \times \left(1 + 0.3\right) \]

\[ 169 = CP \times 1.3 \]

Now, we can solve for CP:

\[ CP = \frac{169}{1.3} = 130 \]

### Step 2: Find the New Selling Price (SP) for 40% Profit
Now that we have the cost price (CP = Rs. 130), we need to find the selling price (SP) for a 40% profit.

Using the same formula:

\[ SP = CP \times \left(1 + \frac{Profit\%}{100}\right) \]

Substituting the new profit percentage:

\[ SP = 130 \times \left(1 + \frac{40}{100}\right) \]

\[ SP = 130 \times 1.4 \]

Calculating this gives:

\[ SP = 182 \]

### Step 3: Calculate the Percentage Increase in Selling Price
Now we need to find out how much the selling price has increased from Rs. 169 to Rs. 182.

The increase in selling price is:

\[ Increase = New\ SP - Old\ SP = 182 - 169 = 13 \]

To find the percentage increase:

\[ Percentage\ Increase = \left(\frac{Increase}{Old\ SP}\right) \times 100 \]

Substituting the values:

\[ Percentage\ Increase = \left(\frac{13}{169}\right) \times 100 \]

Calculating this gives:

\[ Percentage\ Increase \approx 7.69\% \]

### Final Answer
The percentage increase in the selling price to earn a profit of 40% is approximately **7.69%**.

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