for these type of questions drawing venn diagrams

let studying only Aeronautics ,Biotech and Cryogenic be a,b,c

studying both A and B but not c=d

studying both B and C but not a=e

studying both A and C but not b=f

studying all 3 be x

to maximise x everything else must be minimised

Now for 3rd question given cryogenics =100 => And B but not C =100

in order to do this the situation would be

d= x+1 (exactly two>exactly three ) (we maximised d and not e and f cause we wanted to minimise a and b)

e=0,f=0

only A,a =b+1, only b =b, cause A > B (x+x+1+b+1>x+x+1+b )

now C>A=> (x+a+d+1>x+a+d)=>only c= d+a+1=> total C =x+x+1+b+2

we have 2 equations

x+x+1+b+2=100

2x+b=97---------------(2)

2x+b+3 +x+1+2b+1=20

3x +3b =195-----------(1)

solving x=32