A dealer buys goods at 15percent off the list price He want to make a profit of 20percent after allowing a discount of 10percent At what percent above the list price of the dealer should he mark the goods
Answers
Answer:
The dealer should mark his goods at 13.33 per cent more than the list price.
Step-by-step explanation:
LP = List Price
CP = Cost Price
MP = Marked Price
SP = Selling Price
Discount (%) = 20
Profit (%) = 10
Cost Price is 15 per cent off the list price
=> CP is 15% lower than LP
=> CP = LP - 15% of LP
=> CP = LP - 0.15*LP
=> CP = 0.85*LP ............(i)
He needs to make a profit of 20%
=> His selling price has to be 20% more than his cost price
=> SP = 20% more than CP
=> SP = CP + 20% of CP
=> SP = CP + 0.2*CP
=> SP = 1.2*CP .........(ii)
He allows a discount of 10 per cent
=> His selling price is 10 per cent lower than marked price
=> SP = 10% lower than MP
=> SP = MP - 10% of MP
=> SP = MP - 0.1*MP
=> SP = 0.9*MP
=> MP = (1/0.9)*SP ...........(iii)
From (iii), we get:
MP = (1/0.9)*SP
But SP = 1.2*CP ...from (ii)
=> MP = (1/0.9)*1.2*CP
But CP = 0.85*LP ....from (i)
=> MP = (1/0.9)*1.2*0.85*LP
=> MP = [(1.2*0.85)/0.9]*LP
=> MP = 1.1333*LP
=> MP = LP + 0.1333*LP
=> MP = LP + (13.33/100)*LP
=> MP = LP + 13.33% of LP
=> MP is 13.33% more than LP
The dealer should mark his goods at 13.33 per cent more than the list price.
Verification:
Let LP = 100 then MP = 13.33% more than 100 = 113.33
SP = 10% discount over MP = 0.9*MP = 0.9*113.33 = 102
CP = 15% lower than LP = 0.85*LP = 0.85*100 = 85
Profit = SP - CP = 102 - 85 = 17
Profit% = 100*(Profit/CP) = 100*(17/85) = 100*(1/5) = 100/5 = 20
He makes a profit of 20 per cent, as given. ......hence, verified.
Answer:
13.33% the MP should be above the LP to gain 20% gain.
Step-by-step explanation:
List price = LP
Marked price = MP
Selling price = SP
Now let's solve the sum
Let LP be x
Then CP ( discount = 15%)
= x-15x/100
=85x/100
=17x/100
Now
Dealers CP = 17x/100
Dealers SP ( if 20% gain required)
=120/100*17x/20
=6/5*17x/20
=51x/50
Dealers MP ( if 10% discount is offered)
=(100*SP) / (100— discount %)
=(100*51x/50) / 100-10
=51x/50
Therefore,
%above the LP is the MP
= (LP-MP/MP)*100
=(51x/50-x/x)*100
=120/9
=13.3333%
Felling happy after solving the sum.