Problem Solving

Que: A merchant bought 1,000 fans for $15 each. He sold 40 percent of the fans for $20 each and the rest for $30 each. What was the merchant’s average profit per fan?

(A) $11
(B) $15
(C) $18
(D) $21
(E) $26

Solution: Cost price of 1,000 fans = $ (15 * 1000) = $15,000

=> Number of fans sold at $20 each = \(\frac{40}{100}\cdot1,000=400\)

=> Thus, selling price of these 400 fans = $(400 * 20) = $8,000

=> Number of fans sold at $ 30 each = 1000 – 400 = 600

=> Thus, selling of these 600 fans = $(600 * 30) = $18,000

=> Total selling price of 1,000 fans = $8,000 + $18, 000 = $26,000

=> Total profit: Selling price – Cost price = $26,000 - $15,000 = $21,000

=> Profit per fan:$ \(\frac{21,000}{1,000}\) = 21

Therefore, D is the correct answer.

Answer D