X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?  Choose the most appropriate option
A) 3
B) 4
C) 6
D) 9
E) 5

Rationale: investments of x , y and z respectively are rs . 20000 , rs . 25000 and rs . 30000 let investment period of z be x months . ratio of annual investments of x , y and z is ( 20000 * 12 ) : ( 25000 * 12 ) : ( 30000 * x ) = 240 : 300 : 30 x = 8 : 10 : x the share of z in the annual profit of rs . 50000 is rs . 14000 . = > [ x / ( 18 + x ) ] 50000 = 14000 = > [ x / ( 18 + x ) ] 25 = 7 = > 25 x = 7 x + ( 18 * 7 ) = > x = 7 months . z joined the business after ( 12 - 7 ) months . i . e . , 5 months . answer : e
Answer: E