Question

$A$ is thrice as good a work man as $B$ and takes $60$ days less than $B$ for doing a job. Find the time in which they can do it together.

• A. $15\frac{9}{3}$
• B. $22\frac{4}{9}$
• C. $15\frac{7}{4}$
• D. $22\frac{1}{2}$

Answer 1

The correct option is D $22\frac{1}{2}$

Ratio time taken by A and B=$1:3$

The time difference is $(3-1)=2$ days while B takes 3 days and A takes 1 day

If difference of time $2$days, B takes $3$ days

If difference of time 60 days, B takes $\frac{3\times 60}{2}=90$ days

So A takes $30$ days to do work

So A one day work=$\frac{1}{30}$

And B one day work =$\frac{1}{90}$

So A + B one day work=$\frac{1}{30}+\frac{1}{90}=\frac{4}{90}=\frac{2}{45}$

So the work takes $\frac{45}{2}=22\frac{1}{2}$days