The marked price of an article is increased by `25%` and the selling price is increased by `16.66%`, then the amount of profit doubles. If the original marked price be ₹ 400 which is greater than the corresponding cost price by `33.33%`, what, is the increased selling price?

Options

A. 240
B. 360
C. 420
D. 600

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (CP)

Given that the marked price (MP) is ₹400 and it is greater than the cost price (CP) by 33.33%, we can express this relationship mathematically.

Let the cost price be \( CP \).

From the problem, we know:
\[ MP = CP + \frac{1}{3}CP \]
This means:
\[ MP = \frac{4}{3}CP \]

Substituting the given marked price:
\[ 400 = \frac{4}{3}CP \]

To find \( CP \), we can rearrange the equation:
\[ CP = 400 \times \frac{3}{4} = 300 \]

### Step 2: Determine the Original Selling Price (SP)

Next, we need to find the original selling price. The problem states that the selling price is initially unknown, but we know that the profit is given by:
\[ Profit = SP - CP \]

Let’s denote the original selling price as \( SP \). Therefore:
\[ Profit = SP - 300 \]

### Step 3: Calculate the New Selling Price After Increase

The selling price is increased by 16.66%, which is equivalent to \( \frac{1}{6} \). Thus, the new selling price can be calculated as:
\[ New\ SP = SP + \frac{1}{6}SP = \frac{7}{6}SP \]

### Step 4: Profit Doubles

According to the problem, the profit doubles after the increase in selling price. Therefore, we can set up the equation:
\[ New\ Profit = 2 \times Original\ Profit \]

Substituting the expressions for profit:
\[ \left(\frac{7}{6}SP - 300\right) = 2 \times (SP - 300) \]

### Step 5: Solve for the Original Selling Price (SP)

Expanding the equation:
\[ \frac{7}{6}SP - 300 = 2SP - 600 \]

Rearranging gives:
\[ \frac{7}{6}SP - 2SP = -600 + 300 \]
\[ \frac{7}{6}SP - \frac{12}{6}SP = -300 \]
\[ -\frac{5}{6}SP = -300 \]

Multiplying both sides by -6/5:
\[ SP = 360 \]

### Step 6: Calculate the Increased Selling Price

Now, we can find the new selling price:
\[ New\ SP = \frac{7}{6} \times 360 \]
\[ New\ SP = 420 \]

### Final Answer

The increased selling price is **₹420**.

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