A person is having goods worth Rs. 800. He sells half of them at a profit of 15%. If he wants to gain 30% profit on the whole, at what gain percent he must sell the remaining goods?

A 17.5%

B 25%

C 45%

D 18%

E 40%

Correct Answer: Option C

According to the given information,

Cost price of all goods = Rs. 800

∴ cost price of half the goods = Rs. 400

∵ Half of the goods are sold at 15% gain,

Profit earned = 15% of Rs. 400 = 0.15 × 400 = Rs. 60

∵ He needs to get 30% profit on the entire lot of goods.

∴ Net Profit Required = 30% of Rs. 800 = 0.3 × 800 = Rs. 240

⇒ Profit required on remaining half of the goods = 240 – 60 = Rs. 180

Selling Price = Rs. 400 + Rs. 180 = Rs. 580

\(\therefore \;\% \;Profit\; = \;\frac{{Selling\;Price - Cost\;Price}}{{Cost\;Price}} \times 100 = \;\frac{{180}}{{400}} \times 100\; = \;45\)