A alone can do a work in 20 days. A and B together can do the same work in 15 days. B and C together can do the same work in $$\frac{75}{2}$$ days. What is the ratio of the efficiency of A, B and in terms of doing the work?

if x and y are no of days taken by A and B respectively then 

work done by A and B = $$\frac{1}{x}$$+$$\frac{1}{y}$$

total time taken = $$\frac{x+y}{xy}$$

work done by A in 1 day =$$\frac{1}{20} $$ 

work done by A and B in 1 day = $$\frac{1}{15} $$ 

work done by B in 1 day = $$\frac{1}{15} $$ - $$\frac{1}{20} $$  = $$\frac{1}{60} $$ 

work done by B and C in 1 day = $$\frac{2}{75} $$ 

work done by C in 1 day = $$\frac{2}{75} $$ - $$\frac{1}{60} $$ = $$\frac{1}{100} $$

ratio of efficiencies A: B : C is ratio of work done by A:B:C

$$\frac{1}{20} $$ : $$\frac{1}{60} $$ :$$\frac{1}{100} $$

$$15 : 5 : 3$$