Dear Ashif
 
To find the atomic weight for the elements A and B, we will use the following formulas:
Moles = mass/ molar mass.....molar mass= mass/moles
Hence you can calculate the molar mass of the compounds B2A3 and B2A using the above formulas.
B2A3 .....  molar mass =  9g/ 0.05 
                                    =  900/5   = 180
     Therefore relative formula mass of B2A3= 180
that means, (atomic mass A)x 2 + (atomic mass B)x3  =  180
                    2A + 3B = 180
Relative atomic mass of B2A:
molar mass= mass / moles  =    10g/0.1 moles
                                             =    100 u  
            
                   Therefore RAM of B2A= 100
That means,    (atomic mass B)x2 + atomic mass A= 100
                         2B  +  A = 100.....
Solve the two equations by substitution;
B2 + A3 =180
2B + A   = 100  ( A= 100 -2B)
B2 + 3( 100 -2B) = 180
2B + 300 - 6B = 180
2B- 6B = 180-300
 -4B = -120  (divide both sides by -4)
    B  =  30
substitute B to find A
2B + A = 100
(2 x30) + A = 100            60 + A = 100
                                             A = 100 - 60
                                              A = 40
Therefore Atomic weight of A is 40
                                                B is 30
                      
Regards
Arun (askIITians forum expert)