Correct Answer - Option 3 : Only III
Given:
MP = 40% above the CP
SP of 50% goods = MP
Discount on remaining 50% of goods = 10%
Formula Used:
Profit% = (Profit /CP) × 100
Discount% = (Discount /MP) × 100
SP = {(100 + P%)/100} × CP
SP = {(100 – D%)/100} × MP
Where P → Profit, D → discount, CP → cost price, SP → selling price and MP → maximum retail price.
If a quantity is first increased by a% and then by b%, then it is equivalent to a single change of
(a + b + ab/100)%
Calculation:
50% of goods are sold at MP
⇒ Profit on 50% goods = 40%
Remaining 50% sold at a 10% discount
CP is first increased by 40% and then decreased by 10%
Profit = 40 – 10 – (40 × 10)/100
⇒ 40 – 10 – 4
⇒ 26%
Total gain on 100% goods = (40 × 50 + 26 × 50)/100
⇒ (40 + 26)/2
⇒ 66/2
⇒ 33%
I. His overall percentage gain is 70%
His overall percentage gain is 33%
⇒ I is incorrect
II. 40% < overall percentage gain < 50%
33% < 40% < 50%
⇒ II is incorrect
III. Overall percentage gain is a multiple of 11
Overall percentage gain = 33%
⇒ 3 × 11%
⇒ III is correct
∴ Only III is correct.