The ratio of boarders to day scholars at a school is 7 to 16. However, after a few new students join the initial 560 boarders, the ratio changed to 1 to 2, respectively. If no boarders became day scholars and vice versa, and no students left the school, how many boarders joined the school? Choose the correct choice from the following choices:
A) 48
B) 64
C) 70
D) 80
E) 84

Rationale: let day scholars be ds and boarders be b given b / ds = 7 / 16 - - - > eq 1 initially b = 560 and x be new boarders joined then from eq 1 , we get ds = 16 / 7 * 560 = 1280 now , new ration is 560 + x / ds = 1 / 2 560 + x / 1280 = 1 / 2 = > 1120 + 2 x = 1280 = > 2 x = 160 = > x = 80 ans option d
Answer: D