The ratio of the efficiencies of A, B and C is 7 : 5 : 4. Working together, they can finish a work in 35 days. A and B work together for 28 days. The remaining work will be completed (in days) by C alone:

As per the given question,

Ratios in the efficiencies of A, B and C are $$7:5:4$$

So, A can finish the work in $$=\dfrac{x}{7}$$ days

B can finish the work in $$=\dfrac{x}{5}$$ days

C can finish the work in $$=\dfrac{x}{4}$$ days

So, If they are working together, then they can finish the work in one days$$\dfrac{7}{x}+\dfrac{5}{x}+\dfrac{4}{x}=\dfrac{1}{35}$$

$$\dfrac{16}{x}=\dfrac{1}{35}$$

$$x=16\times 35$$

Now, If A and B are working together, then they can finish the work in one day $$=\dfrac{7}{x}+\dfrac{5}{x}=\dfrac{12}{x}$$

They worked together for 28 days, Hence they will finish the total work $$=\dfrac{12\time 28}{16\times 35}=\dfrac{3}{5}$$

Hence the remaining work $$=1-\dfrac{3}{5}=\dfrac{2}{5}$$

C alone can finish the work in $$=\dfrac{x}{4}=\dfrac{16\times 35}{4}=140$$days

Hence C alone can finish the remaining work $$=\dfrac{140\times 2}{5}=28\times 2= 56$$days.