algebra precalculus - In how many days can A alone finish the work?

A and B can do a piece of work in 40 days. After working for 10 days they are assisted by C and work is finished in 20 days more. If C does as much work as B does in 3 days, in how many days A alone can do the work?

Here is my approach, please let me know which step is wrong. As the answer is 432 days and I am getting nowhere close to it. Thank you.

My approach-
A, B and C are per day work done by each of them.
$40A + 40B = 1$
3/4th work done in remaining 20 days when assisted by C,
$20A + 20B + 20C = 3/4$
Also, it's given that,
$C = 3B$
Solving these 3 equations I am getting,
$A = 1/48$
So,
$48A = 1$
Hence, A takes 48 days to finish the whole work by himself.
But the answer is 432. Please help. Thank you.