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If the selling price of a refrigerator is 26% more than its cost price and the discount offered on its marked price is 4%, then which of the following is correct? I. The ratio of its selling price to the cost price is 63 ∶ 50 II. The ratio of its cost price to the marked price is 7 ∶ 4 III. The ratio of its marked price to the cost price is 21 ∶ 16

If the selling price of a refrigerator is 26% more than its cost price and the discount offered on its marked price is 4%, then which of the following is correct? I. The ratio of its selling price to the cost price is 63 ∶ 50 II. The ratio of its cost price to the marked price is 7 ∶ 4 III. The ratio of its marked price to the cost price is 21 ∶ 16 Correct Answer I and III 

Given:   

Profit% = 26%

Discount% = 4%                         

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 = 4 and P = 26

⇒ CP/MP = 96/126

⇒ 16/21

⇒ MP ∶ CP = 21 ∶ 16

SP = {(100 + 26/100} × CP

SP = (126/100) × CP

⇒ SP = (63/50) × CP

⇒ SP/CP = 63/50

⇒ SP ∶ CP = 63 ∶ 50

Only II is not correct

∴ I and III are correct.

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