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.