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 answers.
A) 48
B) 64
C) 70
D) 80
E) 84
Let day scholars be 80S and boarders be B   Given B/80S = 7/16 ---&gt; eq1   Initially B = 560 and x be new boarders joined   Then from eq1 , we get 80S = 16/7*560= 
<gadget id="calculator">16/7*560</gadget>
<output>1_280</output>
1280   Now , new ration is 560+x / 80S= 1/2   560+x / 1280 = 1/2 =&gt; 1120+2x = 1280 =&gt; 2x = 160 =&gt; x = 80   ANS option 80
<result>D</result>
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?