A and B together can do a piece of work in 12 days which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days B could finish the work ?

Let us assume the total work to be done as 48 units.
Let the capacities of A be a, B be b and C be c.
12(a+b) = 48 => a+b = 4 ----------(1)
16 (b+c) = 48 => b+c = 3.-----------(2)
5a+7b+13c = 48 (Given in the question). ------------(3)

(1) x 5 + (2) x 13 => 5a + 5b + 13b + 13c =20+39
5a+18b+13c = 59 ----------------------------(4)
(4) - (3) => 11b = 11
b = 1
Therefore, b can complete the work in 48 days. Option A is the right answer.