Correct Answer - Option 2 : 39
A is twice as good a workman as B and together they finish a piece of work in 13 days.
Efficiency ∝ 1/Time
The efficiency ratio of A and B is 2 : 1
The time ratio of A and B is 1 : 2
Let, A took time x days and B took time 2x days to complete the work alone
In 1 day A can do 1/x part of the work
In 1 day B can do 1/2x part of the work
Together in 1 day they can do 1/13 part of the work
(1/x) + (1/2x) = 1/13
⇒ 3/2x = 1/13
⇒ x = 39/2
B alone will finish the work in 2 × (39/2)
= 39 days
∴ In 39 days B alone will finish the work.