A alone can complete a work in 20 days with full efficiency. If the efficiency of A decreases by 20 percent. then A alone can do the same work in how many days?

25

A = 20 days,

A 's efficiency decreased by 20% = A (Old) : A (New) = 100 : 80 = 5 : 4

⇒ Total work = 5 x 20 = 100 units,  ..(Efficiency × Days = Total work)

⇒ Time required by A to finish work with new efficiency = \(\frac{100}{4}\) = 25 days.     ..(\(\frac{Work}{Efficiency}\) = Time)