The cost price of an article 1 is six times of the profit earned by selling it at SP1. Cost price of article 2 is three times the loss incurred by selling it at SP2. If the cost prices of the articles are the same, then what is the ratio of SP1 and SP2?

In the question given Cost price of article 1 and Cost price of article 2 are same 

let the cost price of both the article be CP 

cost price of article1 is 6 times profit earned by selling article at SP1  

that is CP = $$6\times profit$$

we know the formula SP = CP + profit therefore profit = SP-CP

now profit = SP1- CP 

CP = $$6\times \left(SP1- CP\right)$$

CP = 6SP1 - 6CP =  6SP1= 7CP 

SP1= $$\frac{7}{6}CP$$

cost price of article2  is 3 times  loss occured by selling article at SP2 

that is CP = $$3\times loss$$

we know that SP = CP -loss  therefore loss = CP-SP

CP = $$3\times \left(CP-SP2\right)$$

CP= 3CP - 3SP2 = 3SP2 = 2CP 

SP2= $$\frac{2}{3}CP$$

$$\frac{SP1}{SP2}$$= $$\frac{\frac{7}{6}CP}{\frac{2}{3}CP}$$= $$\frac{7}{4}$$

hence SP1:SP2 is 7:4