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.**