Question

to complete a work A takes 50% more times than B . If together take 18 days to complete the work . How much time shall B take to do it?​

Answer 1

Given :-

• A takes 50% more times than B If together they take 18 days to complete the work.

To find :-

• How much time shall B take to do it

Solution :-

Let the work complete by B be x days

then,

work done by B in 1 day = $\rm\dfrac{1}{x}$

A can do the work in = $\rm\:x+\dfrac{50}{100}x$

A can do the work in =$\rm\:x+\dfrac{x}{2}$

A can do the work in = $\rm\dfrac{2x+x}{2}$

A can do the work in = $\rm\dfrac{3x}{2}\:days$

work done by A in 1 day = $\rm\dfrac{2}{3x}$

work done by A and B = 18 days

work done by A and B in 1 day = $\rm\dfrac{1}{18}$

According to the above values,

$\rm\:\dfrac{1}{x}+\dfrac{2}{3x}=\dfrac{1}{18}$

$\rm\longrightarrow\:\dfrac{3+2}{3x}=\dfrac{1}{17}$

$\rm\longrightarrow\:\dfrac{5}{3x}=\dfrac{1}{18}$

$\rm\longrightarrow\:3x=5\times{18}$

$\rm\longrightarrow\:3x=90$

$\rm\longrightarrow\:x=\cancel\dfrac{90}{3}$

$\rm\longrightarrow\:x=30$

Hence,B can complete the work in 30 days.