Question

A works twice as fast as $\mathrm{B}$. If $\mathrm{B}$ can complete a work in $12$ days independently then the number of days in which $\mathrm{A}$ and $\mathrm{B}$ can together finish the work is?

Answer 1

Step 1: To determine the A and B work individually

B can complete a work in $12$days independently.

The speed of A is twice the speed of B.
Now, as given B can complete a work in $12$ days, so the work done by B in one day will be ${\displaystyle \frac{1}{12}}$
Now, the work done by A in one day will be

${\displaystyle \frac{2}{12}}={\displaystyle \frac{1}{6}}$ (as given A works twice as fast as B)

Step 2: To determine the A and B work together

When A and B work together the work done by them in one day will be

$\Rightarrow \frac{1}{12}+\frac{1}{6}$

By taking L.C.M, we get

$$\begin{gathered} \Rightarrow \frac{1+2}{12} \\ \Rightarrow \frac{3}{12} \\ \Rightarrow \frac{1}{4} \end{gathered}$$
It means when A and B work together they complete the work in $4$ days.