Question

A can do a work in $12$ hours, B can do in $14$ hours. They work alternatively starting from $A$. $A$earns Rs.$15/hr$. How much does he earn from the whole job?

Answer 1

Given that

$NumberofhoursinwhichAcanfinishajob=12hours$

$NumberofhoursinwhichBcanfinishajob=14hours$

They work alternatively starting from $A$.$A$ earns Rs.$15/hr$
Work done

$Totalwork=L.C.M$of (A’s hours, B’s hours)

$=L.C.M.of(12,14)=84units$

$NumberofunitsdonebyA=84/12=7$

$NumberofunitsdonebyB=84/14=6$

Since $A$ and $B$ working alternatively starting with $‘A\text{'}$’.

So, $7+6=13$ units done in $2$days by $A$and $B$ alternatively.

And we need to do $84$ units of work.

First, we will try to find the multiple of $13$ which is nearest to $84$. i.e. $78$ units.