question on profit- loss?

Question

By selling a radio at 2/5 of marked price there is a loss of 20% .If the radio is sold at the marked price , profit per cent will be..?

Answer 1

Let c be the cost of the radio and p be the marked price.

"By selling a radio at 2/5 of marked price there is a loss of 20%" tells you that:

2p/5 = .8c

Since we want to know the percent profit when the radio is sold at the marked price, we need to solve for p to get:

p = 2c

So the profit is 2c - c = c = 100% of the cost.

Answer 2

Let the marked price of the radio be $100
Selling Price=2/5 of $100
=$40
By selling the radio at $40,there was a loss of 20%
Hence Cost Price=$40*(100/80)
=$50
%age of profit if sold at marked price
=(100-50)*100/50
=100%
Here is another process for solving the problem
Let the C.P. be $100
S.P.=$80
This is 2/5th of Marked price
Hence Marked price=$80*5/2=$200
percentage of profit if sold at marked price
=(200-100)=100%

Answer 3

let p = % profit
c(1 + p/100)(2/5) = c(1 - 20/100)
2/5 + p/250 = 1 - 20/100
100 + p = 250 - 50
p = 100%

2*2c/5 = 4c/5