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The cost price of an article 1 is six times the profit earned by selling it at SP1. The 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?

The cost price of an article 1 is six times the profit earned by selling it at SP1. The 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? Correct Answer 7 : 4

Cost price = CP and Selling price = SP

⇒ CP1 = 6(Profit)

⇒ CP1 = 6 × (SP1 – CP1)

⇒ 7 × CP1 = 6 × SP1

⇒ CP1 = (6/7) SP1      ---- (1)

⇒ CP2 = 3(Loss)

⇒ CP2 = 3(CP2 - SP2)

⇒ 3 SP2 = 2 CP2

⇒ CP2 = 3/2 SP2      ---- (2)

If the cost prices of the articles are the same,

From (1) = (2)

⇒ (6/7) SP1 = 3/2 SP2

⇒ SP1/ SP2 = 7/4

⇒ SP1 : SP2 = 7 : 4

∴ The ratio of SP1 and SP2 is 7 : 4.

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