Problem Solving

Que: A pen company manufactures two types of the pen: Pen A and Pen B. The company manufactures 200 ‘type A’ pens at the beginning of 2015. At the end of each year, starting with 2015, the company retired 50 of the ‘type A’ pens and acquired 75 new ‘type B’ pens. How many years did it take before the number of ‘type A’ pens left in the company was less than 50 percent of the pens?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Solution: 50 percent of pens: \(\frac{50}{100}\cdot200=100\)

=> In 2015, type A pen = 200
=> Type B pen = 0

=> In 2016, type A pen = 200 – 50 = 150
=> Type B pen = 75

=> In 2017, type A pen = 150 – 50 = 100
=> Type B pen = 75 + 75 = 150

=> In 2018, type A pen = 100 – 50 = 50
=> Type B pen = 225

Therefore, in 3 years, ‘type A’ pen = 100 – 50 = 50 which is 50 percent less than of total ships.

Therefore, B is the correct answer.

Answer B