Question

to complete a work a and b takes 8 days b and c takes 12 days a b and c takes 6 days. how much time a and c will take 24 days 16 days 12 days 8 days answer: option d

Answer 1

A+B 1 day work = 1/8
B+C 1 day work = 1/12
A+B+C 1 day work = 1/6

We can get A work by (A+B+C)-(B+C)
And C by (A+B+C)-(A+B)

So A 1 day work = 
\begin{aligned} 
\frac{1}{6}- \frac{1}{12} \\ 
= \frac{1}{12} 
\end{aligned}

Similarly C 1 day work = 
\begin{aligned} 
\frac{1}{6}- \frac{1}{8} \\ 
= \frac{4-3}{24} \\
= \frac{1}{24} 
\end{aligned}

So A and C 1 day work =

\begin{aligned} 
\frac{1}{12} + \frac{1}{24} \\ 
= \frac{3}{24} \\
= \frac{1}{8} 
\end{aligned}

So A and C can together do this work in 8 days