X is \(\frac{8}{5}\) times as efficient as Y. If X can complete \(\frac{4}{5}\)th of the work in 24 days. What fraction of the same work would remain incomplete if Y alone works on it for 32 days only?

33.33%

X × \(\frac{4}{5}\) = 24

X = 30 days  (X will take 30 days to complete the work)

                          X   :    Y

Efficiency     ⇒    8   :    5

No. of days ⇒    5   :   8

                         ↓        ↓

                        ×6     ×6

                         ↓        ↓

                       30      48

Y worked for 32 days = \(\frac{32}{48}\) = \(\frac{2}{3}\)rd work is done.

Incomplete work = 1 - \(\frac{2}{3}\) = \(\frac{1}{3}\)

Percentage of incomplete work = \(\frac{1}{3}\) × 100 = 33.33%