Question

$A$ and $B$ can dig a trench in $20$ days. If $B$ is twice as good as $A$ in his work, in how many days can A alone complete the work?

Answer 1

( $A^{\prime }s$ one day work $=B^{\prime }s\frac{1}{2}$ days work )

$A$ is twice as good as $B$.

Let $B=x,A=2x$

$A$ and $B$ can complete the work together in $20$ days.

So,$(A+B{)}^{\prime }s20$ days’ work$=1$

$(A+B{)}^{\prime }s1$ day’s work$=1/20$

So,

$x+2x=\frac{1}{20}$

$3x=\frac{1}{20}$

$x=\frac{1}{60}$

$2x=\frac{1}{30}$

A’s one day’s work$=1/30$

A can complete the work alone in $30$ days.

$\therefore answeris30$