As I understand the trasaction B's bill is for 10000/- so he gets Rs 9000 as a cheque/ cash and rs 1000/- goes to Tds which he can claim while filing return.
B pays assignment fees (?) to C. Is C's bill is 9000? Then Rs 900 is deducted which he can claim later and 8100/- paid to him.
Where is the question of double deduction?