(a) 20 days
Let x, y, z be the one day work of A, B and C respectively.
According to the question,
For the first three days, A, B, C work together.
⇒ 3(x + y + z) =
= 37% of the work.
∴ Remaining work = 63%
Thus, 7 (x + y) =
⇒ x + y =
= 9 %
We know that, 5x = 4y (given)
⇒ x = 4 % and y = 5%
In 3 days (A + B + C) do 37% of the work.
⇒ 3x + 3y + 3z = 37%
⇒ 3z = 37% - (3 x 4)% - (3 x 5)%
= (37 - 12 - 15)% ≈ 10%
∴ z = 3.33%
Hence, B is the fastest and require 20 days to complete the work.