**Answer with Explanation:**

**Ratio of times taken by A and B = 100 : 130 = 10 : 13.**

Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x => x = (23 x 13/10) => x =299/10 .

A's 1 day's work = 1/23 ;

B's 1 day's work = 10/299 .

(A + B)'s 1 day's work = (1/23 +10/299) = 23/299 = 1/13 .

Therefore, A and B together can complete the work in 13 days.

Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x => x = (23 x 13/10) => x =299/10 .

A's 1 day's work = 1/23 ;

B's 1 day's work = 10/299 .

(A + B)'s 1 day's work = (1/23 +10/299) = 23/299 = 1/13 .

Therefore, A and B together can complete the work in 13 days.