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 what time would C alone do it?

(A). \[6\dfrac{2}{3}\]
(B). \[15\dfrac{17}{19}\]
(C). \[10\dfrac{10}{17}\]
(D). \[11\dfrac{9}{4}\]

Answer 1

- Hint: The important thing that can be used in solving the question is that the
If any person can do a particular work in x days, then the amount of work that the person can do in 1 day is given by \[\dfrac{1}{x}\] .

Complete step-by-step answer:
As mentioned in the question, we know that
Days in which A can do the work is = 10 days
Days in which B can do the work is = 18 days
Days in which (A + B + C) can do the work is = 4 days
Now, we know the time taken by A, B and all three of them, so
Amount of work done by A in 1 day \[=\dfrac{1}{10}\]
 Amount of work done by B in 1 day \[=\dfrac{1}{18}\]
Amount of work done by (A+B) in 1 day
\[\begin{align}
  & =\dfrac{1}{10}+\dfrac{1}{18}~ \\
 & =\dfrac{18+10}{18\times 10} \\
 & =\dfrac{28}{180} \\
 & =\dfrac{7}{45} \\
\end{align}\]
 Amount of work done by (A+B+C) in 1 day \[=\dfrac{1}{4}\]
\[\therefore Amount\ of\ work\ done\ by\ C\ in\ 1\ day=~\ \dfrac{1}{4}-\dfrac{7}{45}=\dfrac{17}{180}\]
\[\therefore C\ can\ do\ the\ work\ in\text{ }=\text{ }\dfrac{180}{17}\text{ }days=10\dfrac{10}{17}\ days\]

Note: The students can make an error when they do not consider this fact that
If any person can do a particular work in x days, then the amount of work that the person can do in 1 day is given by \[\dfrac{1}{x}\] .
For getting to the solution, the students must know that work and time are directly proportional quantities which mean that if one of these two quantities increases then the other one would increase as well.