Correct Answer - Option 4 : 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.**