The marked price of an item is 25% above its cost price. A shopkeeper sells it, allowing a discount of x% on the marked price. If he incurs a loss of 8%, then the value of x is___

The marked price of an item is 25% above its cost price. A shopkeeper sells it, allowing a discount of x% on the marked price. If he incurs a loss of 8%, then the value of x is

A. 26.4%

B. 26.8%

C. 25.6%

D. 25.2%

Let’s denote the cost price of the item as CP. The marked price (MP) is given as 25% above the cost price, so:

\[ MP = CP + 0.25 \times CP = 1.25 \times CP \]

Now, the shopkeeper sells the item with a discount of x% on the marked price. Therefore, the selling price (SP) can be expressed as:

\[ SP = MP – \frac{x}{100} \times MP \]

The shopkeeper incurs a loss of 8%, so the selling price is 92% of the cost price:

\[ SP = 0.92 \times CP \]

Now, equate the two expressions for SP:

\[ 1.25 \times CP – \frac{x}{100} \times 1.25 \times CP = 0.92 \times CP \]

To solve for x, first, cancel out the common factor of CP:

\[ 1.25 – \frac{x}{100} \times 1.25 = 0.92 \]

Now, isolate x:

\[ \frac{x}{100} \times 1.25 = 1.25 – 0.92 \]

\[ x = \frac{1.25 – 0.92}{1.25} \times 100 \]

\[ x \approx 26.4 \]

So, the value of x is approximately 26.4%. Therefore, the discount percentage is approximately 26.4%.

Leave a Reply

Your email address will not be published. Required fields are marked *