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?

7 : 4

According to the question,

= CP₁ = 6(Profit)

= CP₁ = 6 × (SP₁ – CP₁)

= 7 × CP₁ = 6 × SP₁

= CP₁ = (\(\frac{6}{7}\) ) SP₁      ---- (a)

= CP₂ = 3(Loss)

= CP₂ = 3(CP₂ - SP₂)

= 3 SP₂ = 2 CP₂

= CP₂ = (\(\frac{3}{2}\) ) SP₂      ---- (b)

According to the question,

If the cost prices of the articles are the same,

Put (a) = (b)

= (\(\frac{6}{7}\) ) SP₁ = (\(\frac{3}{2}\) ) SP₂

= SP₁ : SP₂ = 7 : 4