Question

At what percentage above the C.P. must an article be marked so as to gain 33% after allowing a customer a discount of 5%? ​

Answer 1

Let the Marked price of the article = x,

Since, the discount percentage = 5 %,

⇒ The discount = 5% of marked price = 5 % of x = 0.05x

Thus, the selling price = Marked price - Discount = x - 0.05 x = 0.95x,

According to the question,

Profit % = 33 %,

33 % more than cost price = Selling price,

133 % of C.P. = 0.95 x

⇒ C.P. × 133/ 100 = 0.95 x

⇒ C.P. = $\dfrac{0.95x\times 100}{133}$ =$\dfrac{95x}{133}$

Hence, the percentage by which marked price is above the cost price

=$\dfrac{\text{Marked price - Cost price }}{\text{ cost price }}$

=$\dfrac{x-95x-133}{95x-133}$

=$\dfrac{38x}{95x}\times 100=\dfrac{3800}{95}$

=40%