let total work = 1

A and B are working alternately with B start first

total work time=34/3=11 +1/3 days

for 5 -5 days both will work .on 11th day B will work and A will work for next \(\frac{1}{3}\)rd day . 

Thus B works for =6 days and A works for 5+1/3 days

A can complete the work in 48 days

A's 1 day work = \(\frac{1}{48}\)

A's \(\frac{16}{3}\) day work =\(\frac{16}{48 × 3}\)

= \(\frac{1}{9}\)

So B’s work in 6 days= \(\frac{8}{9}\)

B’s per day work=\(\frac{8}{54}\) = \(\frac{4}{27}\)

So for B the days required to complete 4 time work

=\(\frac{27 × 4}{4}\)  = 27 days