A mark an article 60% above its cost price. When he allows 4d% discount on marked price he earns 28% profit. If he allows 6d% discount, then find the profit/ or loss %?

The correct answer is 12% (or Option 12%).

Let us solve the problem step-by-step.

Step 1: Define the Cost Price (CP) and Marked Price (MP)
Let the Cost Price (CP) of the article be 100 units.
Since the article is marked 60% above its cost price, we calculate the Marked Price (MP) as follows:

$\text{MP}=100+(60\%\text{of}100)=160$

Step 2: Find the Selling Price and discount rate in the first scenario
In the first scenario, a discount of 4d% is allowed on the marked price, and a profit of 28% is earned.
Since profit is 28%, the Selling Price (SP₁) is:

${\text{SP}}_1=100+28=128$

The discount amount in the first scenario is the difference between MP and SP₁:

$\text{Discount}=160-128=32$

Discount percentage is given by:

$\mathrm{4d}\%=\left(\frac{32}{160}\right)\times 100\%=20\%$

From $\mathrm{4d}=20$, we find:

$d=5$

Step 3: Calculate the discount and new Selling Price in the second scenario
In the second scenario, a discount of 6d% is allowed.
Substitute $d=5$ into 6d%:

$\text{New Discount \%}=6\times 5\%=30\%$

Now, calculate the new Selling Price (SP₂) after a 30% discount on the Marked Price (160):

${\text{SP}}_2=160-(30\%\text{of}160)$

${\text{SP}}_2=160-48=112$

Step 4: Find the final Profit Percentage
Since the Cost Price (CP) is 100 and the new Selling Price (SP₂) is 112, the profit amount is:

$\text{Profit}=112-100=12$

The Profit Percentage is:

$\text{Profit \%}=\left(\frac{12}{100}\right)\times 100\%=12\%$

Hence, the profit percentage is 12%.