A is 50% more efficient than B and C is 40% less efficient than B. Working together, they can complete a task in 20 days. In how many days will C alone complete 30% of that task ?

Let B can finish the work in x days,

So, B can finish the work in 1 day $$=\dfrac{1}{x}$$days

As per the question,

If they are working together, then they can finish the work in 20 days.

So, working together, they can finish the work in $$=\dfrac{1}{20}$$ days

A is 50% more efficient than B, so A will finish the work in $$=\dfrac{50x}{100}=\dfrac{x}{2}$$ days

A can finish the work in one day $$=\dfrac{2}{x}$$

C is 40% less efficient than B, so C will finish the work in $$=\dfrac{140x}{100}=1.4x$$ days

C can finish the work $$=\dfrac{1}{1.4x}$$

If they are working together, then they can finish the work in one day $$=\dfrac{1}{x}+\dfrac{2}{x}+\dfrac{10}{14x}=\dfrac{1}{20}$$

$$\Rightarrow \dfrac{14+28+10}{14x}=\dfrac{1}{20}$$

$$\Rightarrow \dfrac{52}{14x}=\dfrac{1}{20}$$

$$\Rightarrow x=\dfrac{52\times 20}{14}=\dfrac{520}{7}$$

Hence, C will finish the work in $$1.4\times \dfrac{520}{7}=104$$ days

Hence, C will be able to finish the work in $$=\dfrac{30 \times 104}{100}=31.2 days \cong 31days$$