If the number of divisions is d, then each division gets 240/d reams. If there were d+4, then 240/(d+4)=⅘(240/d).
So 1/(d+4)=4/5d. 5d=4(d+4), 5d=4d+16, d=16.
CHECK
240/16=15 reams for each of 16 divisions. ⅘ of 15=12 reams for each of 20 divisions.
Note that the number of divisions is independent of the number of reams of paper. The same answer would apply if there has been 2000 reams: 16×125=20×100=2000, 100/125=⅘.
If f is the number of financial institutions, 6/f million dollars is the individual contribution. For f+2 institutions the individual contribution is 6/f-0.5 million dollars.
Therefore, f(6/f)=(f+2)(6/f-0.5), 6=6-0.5f+12/f-1, 0=-0.5f+12/f-1, 0=-0.5f²+12-f, 0=f²+2f-24=(f+6)(f-4).
Since f cannot be negative, f=4.
CHECK
Each institution contributes 6/4=3/2=$1.5m (4 institutions). If there were 6 institutions their individual contribution would be $1m. 4×1.5=6×1=$6m.