The efficiencies of A, B and C are in the ratio 5 : 3: 8. Working together they can complete a work in 30 days. A and B worked together for 20 days. The remaining work will be completed by C alone in:

It is given that,

The efficiencies of A, B, and C = 5:3:8

So, the time is taken by A, B, and C to complete the work$$ =\dfrac{1}{5}:\dfrac{1}{3}:\dfrac{1}{8}$$

So, A can finish the work in $$\dfrac{x}{5}$$

A can finish the work in one day $$\dfrac{5}{x}$$

B can finish the work in $$\dfrac{x}{3}$$

B can finish the work in one day $$\dfrac{3}{x}$$

C can finish the work in $$\dfrac{x}{8}$$

C can finish the work in one day $$\dfrac{8}{x}$$

A, B and C can finish the work in one days $$\dfrac{5}{x}+\dfrac{3}{x}+\dfrac{8}{x}=\dfrac{1}{30}$$

$$\Rightarrow \dfrac{16}{x}=\dfrac{1}{30}$$

$$\Rightarrow x=16\times 30 =480$$

So, A can finish the work in $$\dfrac{480}{5}=96$$days

B can finish the work in $$\dfrac{480}{3}=160$$days

C can finish the work in $$\dfrac{480}{8}=60$$days

If A and B are working together, then they can finish the wok in one days $$=\dfrac{1}{96}+\dfrac{1}{160}=\dfrac{5+3}{480}=\dfrac{8}{480}$$

Hence, they can finish the work in 20 days $$=\dfrac{8\times 20}{480}=\dfrac{1}{3}$$

Hence, the remaining work $$=1-\dfrac{1}{3}=\dfrac{2}{3}$$

So, C will finish the work $$=60\times \dfrac{2}{3}=40 days$$