If a trader sells an item at 5% profit, it will be Rs. 50 more than if he sells it at a loss of 55%. Find out the starting price of the item.
Answers
Step-by-step explanation:
Given :-
A trader sells an item at 5% profit, it will be Rs. 50 more than if he sells it at a loss of 55%.
To find:-
Find out the starting price of the item ?
Solution:-
Let the cost Price be Rs. X
Profit in it = 5%
Selling Price = [(100+g)×CP]/100
=> SP =( (100+5)×X)/100
=> SP = 105X/100
=> SP= 21X/20
Selling Price of the item = Rs. 21X/20
and given that
If he sells it at 55% of loss then
SP = [(100-l)×CP]/100
=> SP =( (100-55)×X)/100
=> SP = 45X/100
=> SP = 9X/20
Selling Price of the item = Rs. 9X/20
Given that
If a trader sells an item at 5% profit, it will be Rs. 50 more than if he sells it at a loss of 55%.
Selling Price with profit = Selling Price with loss +50
=>21X/20 = (9X/20)+50
=>(21X/20)-(9X/20) = 50
=> (21X-9X)/20 = 50
=> 12X/20 = 50
=> 3X/5 = 50
=> 3X = 50×5
=> 3X = 250
=> X = 250/3
=> X = 83.33
Therefore, X = Rs. 83.33
Answer:-
The starting price of the given item is Rs. 83.33
Check:-
Cost price = Rs. 250/3
Profit = 5%
Loss = 55%
Their difference =
=>[ (100+5)×(250/3)-(100-55)×(250/3)]/100
=>[ (250/3)/100][105-45]
=(250/300)×(60)
=> (250×60)/300
=> 15000/300
=> 150/3
=> 50
Verified the given relations in the problem
Used formulae:-
- Selling Price = [(100+g)×CP]/100
- SP = [(100-l)×CP]/100