To do a certain work, the ratio of efficiencies of A and B is 13 : 11. Working together, they can complete the same work in 19\(\frac{1}{2}\) days. A alone will complete 75% of the same work in?

27 days

       A     :     B

      13    :     11

Total work = \(\frac{39}{2}\) × 24 = 468

A completed 75% work in = 468 × \(\frac{75}{100}\) × \(\frac{1}{13}\)

                                      = 27 days