Discussion Forum

A, B and C can do a piece of work in 6, 8 and 10 days respectively. They begin to work together. A continues to work till it is finished, B leaves off 1 day before and C leaves off $\frac{1}{2}$ day before the work is finished. In what time is the work finished ?

Answer:

Explanation:

Let the work be finished in $x$ days.

Then, $A$ works for $x$ days.

$B$ works for $(x-1)$ days.

$C$ works for $(x-\frac{1}{2})$ days.

Also $A,B,C$ can do $\frac{1}{6},\frac{1}{8},\frac{1}{10}th$ of work daily, respectively.

From the problem,

$\left[\frac{1}{6}x+\frac{1}{8}(x-1)+\frac{1}{10}\left(x-\frac{1}{2}\right)\right]$ $=1$

(i.e) $\left(\frac{1}{6}+\frac{1}{8}+\frac{1}{10}\right)x-\left(\frac{1}{8}+\frac{1}{20}\right)$ $=1$

$\left(\frac{20+15+12}{120}\right)x-\left(\frac{5+2}{40}\right)$ $=1$

$\frac{47x}{120}$ $=\left(1+\frac{7}{40}\right)$ $=\frac{47}{40}$ $\Rightarrow x=3$

$\therefore$ The work was finished in 3 days.