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If the selling price of a wardrobe is 54% more than its cost price and the discount offered on its marked price is 1%, then which of the following is correct? I. The ratio of its cost price to the marked price is 3 ∶ 7 II. The ratio of its cost price to the selling price is 50 ∶ 77 III. The ratio of its marked price to the cost price is 14 ∶ 9

If the selling price of a wardrobe is 54% more than its cost price and the discount offered on its marked price is 1%, then which of the following is correct? I. The ratio of its cost price to the marked price is 3 ∶ 7 II. The ratio of its cost price to the selling price is 50 ∶ 77 III. The ratio of its marked price to the cost price is 14 ∶ 9 Correct Answer II and III 

Given:   

Profit% = 54%

Discount% = 1%                          

Formula Used:

Profit = SP – CP

Discount = MP – SP

Profit% = (Profit /CP) × 100 

Discount% = (Discount /MP) × 100

SP = {(100 + P%)/100} × CP

SP = {(100 – D%)/100} × MP

Where P is Profit, D is discount, CP is cost price, SP is selling price and MP is maximum retail price.

Calculation:

SP = {(100 + P%)/100} × CP

SP = {(100 – D%)/100} × MP

⇒ {(100 + P%)/100} × CP = {(100 – D%)/100} × MP

⇒ (100 + P%) × CP = (100 – D%) × MP 

⇒ CP/MP = (100 – D%)/(100 + P%)

⇒ Putting D = 1 and P = 54

⇒ CP/MP = 99/154

⇒ 9/14

⇒ CP ∶ MP = 9 ∶ 14

⇒ SP = (154/100) × CP

⇒ SP = (77/50) × CP

⇒ SP/CP = 77/50

⇒ CP ∶ SP = 50 ∶ 77

⇒ Only I is incorrect.

∴ II and III are correct.

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