Question

A can do a piece of work in $10$ days , B in $18$ days and A, B and C together in $4$ days. In how many days will C alone can do it?

• A. $6\frac{2}{3}$
• B. $15\frac{17}{19}$
• C. $10\frac{10}{17}$
• D. $11\frac{9}{4}$

Answer 1

The correct option is C $10\frac{10}{17}$

A can do a piece of work in $10$ days and B do the same work in $18$ days.

Then A can do the work in one day =$\frac{1}{10}$

And B can do the work in one day =$\frac{1}{18}$

Then A & B's one day's work $=\frac{1}{10}+\frac{1}{18}=\frac{7}{45}$

Given A ,B and C did work in 4 days

Then A ,B and C's one day work $=\frac{1}{4}$

$\therefore$ C one day work$=\frac{1}{4}-\frac{7}{45}=\frac{17}{180}$

When only C does work $=\frac{180}{17}=10\frac{10}{17}$ days.