Question

A sold an article to B at a loss of 20% and B sold it to C at a gain of 20%. If C paid Rs.6000 for the article, find the cost price of the article for A.

Answer 1

C's cost price=B's selling price
B sold it at a gain of 20%
therefore B's Cost price=(100*Selling price)/(100+profit%)
                                   = (100*6000)/(100+20)
                                   = 600000/120
                                   = 5000
B's Cost price=A's Selling price   
A's cost price=(100*Selling price)/(100-loss%)
                   =(100*5000)/(100-20)
                   =500000/80
                   = 6250
 Thus,A's Cost price=Rs.6250 

Answer 2

Let the cost price of the article for A = x rupees
Then the cost price for B = x - 20°/. of x [ given that A sold at 20 percent loss to B]
⇒ x- 20x/100
⇒ x - x/5 = 4x/5
∴.C.P for B= 4x/5 rupees 
 Now C.P for C = 4x/5 + 20percent of 4x/5 [ Given that B sold at 20 percent gain to C]
⇒4x/5 +  20*4x/100*5
⇒4x/5 + 4x/25
⇒24x/25
∴C.P for C = 24x/25 rupees
Given that C.P for C =6000 rs
∴24x/25 = 6000
⇒24x = 6000* 25
⇒x = 150000/24
⇒x = 6500 rs
∴C.P for A = x = 6250 Rs

I think it is a bit confusing but if you try you would understand. I really hope you will understand.