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 =$ \left(\dfrac{23 \times 13}{10} \right) $

        x=$ \dfrac{299}{10} $.

As 1 days work =$ \dfrac{1}{23} $;

Bs 1 days work =$ \dfrac{10}{299} $.

$\left(A + B\right)$s 1 days work =$ \left(\dfrac{1}{23} +\dfrac{10}{299} \right) $=$ \dfrac{23}{299} $=$ \dfrac{1}{13} $.

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