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 cp be 100
sp = 100+ 33% of 100
sp = 133
mp = (100/100- discount %) * sp
mp = (100/95)*133
mp = 140
% increase =[ (140-100)/100 ]* 100
% increase = 40%

Answer 2

Answer:

40 %

Step-by-step explanation:

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

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

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

$=\frac{\text{Marked price - Cost price }}{\text{ cost price }}\times 100$

$=\frac{x-95x/133}{95x/133}\times 100$

$=\frac{38x}{95x}\times 100=\frac{3800}{95}=40\%$