Question

A man sells an article at profit of 25%.If he had bought it at 20% less and sold it for 10.50 less, then he would have gained 30%. Find the cost price of the article

Answer 1

Let original cost price = k. Then selling price at 25% profit = 1.25k.

If he had bought at 20% less of the cost price, i.e.,at 80% of cost price, then his cost price would have been = 0.8k. 
Then selling price would be 10.50 less than original selling price 1.25k, his selling price would have been = 1.25k - 10.50.
Therefore his profit would have been = SP - CP = (1.25k - 10.5) - 0.8k 
                                                                           = 0.45k - 10.5.
This profit of (0.45k - 10.5) is on the cost price 0.8k.
Hence profit % = (Profit / CP) x 100
                        = [(0.45k - 10.5) / 0.8k] x 100 = 30
                        or 0.21k = 10.5 ==> k = 10.5 / 0.21 = 50

Answer 2

let the cp=x
 sp at profit of 25%=125x/100=1.25x

if the cp had been 8x/10=0.8x and sp=1.25x-10.50
profit=30% 
ATQ,
0.8x+0.3*0.8x=1.25x-10.50
⇒0.8x+0.24x=1.25x-10.50
⇒1.04x=1.25x-10.50
⇒10.50=0.21
⇒x=1050/21=50
So the cost price of the item is 50