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A trader gives a discount based on the number of articles bought by a customer. He gives a discount of 20% when five articles are bought and a discount of 15% when four articles are bought. If the profit he makes in each condition is the same, then, find the ratio of the marked price to the cost price of the article?

A trader gives a discount based on the number of articles bought by a customer. He gives a discount of 20% when five articles are bought and a discount of 15% when four articles are bought. If the profit he makes in each condition is the same, then, find the ratio of the marked price to the cost price of the article? Correct Answer 5 : 3

The trader gives a discount of 20% when five articles are bought and a discount of 15% when four articles are bought.

Condition I  :

SP = 80% of MP = 0.80MP

⇒ Profit = (0.80MP – CP)         ------ (1)

Condition II  :

SP = 85% of MP = 0.85MP

⇒ Profit = (0.85MP – CP)          ------ (2)

According to question-

⇒ 5 × (0.80MP – CP) = 4 × (0.85MP – CP)

⇒ 4MP – 5CP = 3.4MP – 4CP

⇒ 4MP – 3.4MP = 5CP – 4CP

⇒ 0.6MP = CP

⇒ 6MP = 10CP

⇒ MP/CP = 10/6

⇒ MP  :  CP = 5 : 3

∴ The ratio between the MP and the CP = 5 : 3

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