Question

A trader marks an article 4x% above the cost. He gives a discount of (x + 3)% and gets a profit of (2x – 3)%. If he gives a discount of (2x/3)%, what would be his gain percent?

• A. 0.265
• B. 0.426
• C. 0.562
• D. 0.604
• E. 0.688

Answer 1

The Correct Option is D

To solve this, we'll start by understanding the given data and then follow step-by-step calculations.

Let's establish the known variables:

• The article is marked at \(4x\%\) above the cost price (CP).
• A discount of \((x+3)\%\) is given, leading to a profit of \((2x-3)\%\).
• We need to determine the gain percentage if a discount of \(\frac{2x}{3}\%\) is offered.

Step 1: Derive the equations based on given conditions.

Let the cost price (CP) of the article be \(C\).

The marked price (MP) is given as:

• \(MP = C + \frac{4x}{100} \times C = C \left(1 + \frac{4x}{100}\right)\)

The selling price (SP) after a discount of \((x+3)\%\) is:

• \(SP = MP \left(1 - \frac{x+3}{100}\right)\)

Since it results in a profit of \((2x-3)\%\), we relate SP to CP:

• \(SP = C \left(1 + \frac{2x-3}{100}\right)\)

Solving for x:

• Equating the two expressions:
• \(C \left(1 + \frac{4x}{100}\right)\left(1 - \frac{x+3}{100}\right) = C \left(1 + \frac{2x-3}{100}\right)\)

Cancel \(C\) from both sides and solve for \(x\):

• Simplifying the left-hand side:
• \(1 + \frac{4x}{100} - \frac{(4x)(x+3)}{10000}\)
• Equate and solve the quadratic equation for \(x\).

After solving, we get:

• \((Detailed solution not shown for brevity)\)
• Let's analyze when \(\frac{2x}{3}\%\) discount is applied.

Step 2: Calculate the gain with the new discount.

• New SP when the discount is \(\frac{2x}{3}\%\):
• \(SP = MP \left(1 - \frac{2x/3}{100}\right)\)
• Using the previous relation, gain percent is:
• \(\left(\frac{SP - C}{C}\right) \times 100\%\)

The calculations eventually lead to a gain of \(0.604\%\).

Therefore, the correct answer is 0.604.