Question

Suppose $A$ is twice as good a workman as $B$ and together they can finish a job in $24$ days. How many days $A$ alone takes to finish the job?

Answer 1

$A$ is twice a good workman as $B$

$\therefore B=2A$

It is given that $A$ and $B$ together can finish the job in $24$ days.

$\therefore \frac{1}{A}+\frac{1}{B}=\frac{1}{24}$

Substituting $B=2A$ we get

$\therefore \frac{1}{A}+\frac{1}{2A}=\frac{1}{24}$

$\Rightarrow \frac{2+1}{2A}=\frac{1}{24}$ Taking LCM

$\Rightarrow \frac{3}{2A}=\frac{1}{24}$

Cross multiplying we get,

$\Rightarrow 3\ast 24=2A$

$\Rightarrow A=\frac{72}{2}$

$\Rightarrow A=36$

Therefore $A$ alone can finish the work in $36$ days.