23. A shopkeeper wants to make a profit of 10.2 % after allowing 5% discount to the cus- tomers. What percent above the cost should he mark the price?
Answers
Answer:
Let CP be the Cost Price and SP be the selling Price.
Profit=[SP-CP]/CP
0.102 =[(SP-.05SP)-CP]/CP
0.102=[0.95SP-CP]/CP
0.102CP=0.95SP-CP
0.102CP+CP=0.95SP
1.102CP=0.95SP
SP=[1.102CP]/0.95
SP=1.16CP as the selling price.
Therefore, the item must be increased to 16% for the Selling Price and offer 5 % discount, yet still gaining 10.2 % profit.
Checking:
For example the Cost Price of an item is $ 100 and the Selling Price will be priced with an additional of 16%, to make it at the selling price of $116. Then, with the discount of 5%, the final selling price is now 0.95(116)= $110.20. Calculate if the the profit is 10.2%.
Profit=[110.2–100]/100=10.2/100=0.102
Profit=0.102 x100%= 10.2% OK. So it is proven that if you add 16% to the Cost Price for fixing the Selling Price and then offer 5% discount, there is still a profit of 10.2%
16%
MP=100
Selling price for 10.2% profit=110.2
0.95*(actual mark price)=110.2
actual MP=116
Let cost be 100 , so sale price =110.2 so makes price =110.2/(1-.05)=110.2/.95=116. So marked price should be 16% above cost.
A shopkeeper marks his goods 20% above cost price and allows a discount of 15%. What percent does he gain or lose?
After giving a discount of 25%, a shopkeeper earns 40% profit. The marked price is what percent more than the cost price?
A shopkeeper marks his goods 40% above the cost price but allows 40% discount for cash. What percent of profit or loss does he really make?
What price should a shopkeeper mark on an article costing him Rs. 200 to gain 20% after allowing a discount of 10%?
A merchant allows a discount of 10% for cash payments. At how much percent above the CP must he mark his goods to make a profit of 8%?
According to given problem,
(i) A shopkeeper wants to make a profit of 10.2% after allowing 5% discount to the customer.
(ii) What percent above the cost should he mark the price?
(iii) Let C, M & S denote respectively the cost-price, marked-price & the sell-price.
From (i) & (iii) we get following relations,
S = (1 + 10.2/100)*C = 1.102*C …… (1a)
S = (1 - 5/100)*M = 0.95*M …… (1b)
Hence from (1a) & (1b) we get,
0.95*M = 1.102*C
or M = (1.102/0.95)*C = (551/475)*C
or M = (1 + 76/475)*C = [1 + (7600/475)/100]*C
or M = (1 + 16/100)*C …… (1c)
Therefore it is evident from (1c) that
in order to fulfill the given conditions as described in (i), the marked-price should be 16% above the cost-price. [Ans]
A shop keeper allows 15% discount on the marked price, still he manages to have 7 profit. How much high did he mark his goods above the cost price?
Let m.p be x
D%=15
S.p=x(85/100)=17x/20
P%=7
C.p=(17x/20)(100/107)
=85x/107
Difference=x-85x/107
=22x/107
%=2
[(22x/107)/(85x/107)]100
=440/17
M.p is 25.89% more than c.p
A shopkeeper gains 20% after allowing a discount of 10% on the marked price of an article. What is his profit percent if the article is sold at marked price allowing no discount?
Statement of the given problem,
A shopkeeper gains 20% after allowing a discount of 10% on the marked price of an article. What is his profit percent if the article is sold at marked price allowing no discount?
Let
C & M denote cost-price & marked-price of the given article.
P% denotes the profit percent if the article is sold at marked price allowing no discount.
Hence from above data we get following relations,
(1 + 20/100)*C = (1 - 10/100)*M
or (6/5)*C = (9/10)*M
or M/C = (6/5)/(9/10) = 4/3
(1 + P/100)*C = M
or 1 + P/100 = M/C = 4/3
or P = 100*(4/3 - 1) =100/3 = 33.33
Therefore it is evident from above that if the article is sold
at marked price allowing no discount
then the profit percent = 33.33% [Ans]
A shopkeeper fixed the price of his articles 25% above the cost price. If he sold allowing 5% discount, what is his profit percent?
Your margin on