The ratio of the efficiencies of A, B and C is 3 : 5 : 1. Working together, they can complete a piece of work in 5 days. A and B work together for 3 days. The remaining work will be completed by C alone in?

The ratio of the efficiencies of A, B and C is 3 : 5 : 1

Let the work done by A, B, C is 3 units, 5 units, 1 unit in 1 day respectively.

$$\Rightarrow$$  Work done by A,B,C together in 1 day = 9 units

Working together, A, B, C can complete a piece of work in 5 days.

$$\Rightarrow$$  Total work = 9 x 5 = 45 units

A and B work together for 3 days.

Work done by A and B together in 3 days = (3+5) x 3 = 24 units

Remaining work = 45 - 24 = 21 units

Remaining work will be completed by C who can do 1 unit per day.

$$\therefore\ $$Number of days required for C to complete remaining work = 21 days

Hence, the correct answer is Option D