Question

$A$ can do work in $15$ days and $B$ can do the same work in $20$ days. If $A$and $B$ have done work for $4$ days together, the fraction of work left?

Answer 1

Given

$A$ does work in $15$ Days; $B$ does work in $20$ days

$A$ and $B$ have worked together for $4$ days;

Let the Total work be $W$

$W=TotalWork$;

A's daily work done $=\frac{W}{15}$

B's daily work done$=\frac{W}{20}$

Work done by both on $4$ days$=\left(\frac{W}{15}+\frac{W}{20}\right)x4$

$\frac{W}{15}+\frac{W}{20}$;

LCM of $15$ and $20$

$15=3\times 5$

$20=2\times 2\times 5$

$LCM=2\times 2\times 3\times 5=60$

Sum of Work done by $A$ and $B$ in $4$ days

$\frac{W}{15}=\frac{4W}{60}and\frac{W}{20}=\frac{3W}{60}$

$\frac{(4w+3w)}{60}=\frac{7W}{60}$

$\left(\frac{W}{15}+\frac{W}{20}\right)x4=\left(\frac{7W}{60}\right)x4=\frac{28W}{60}$

$WorkLeft=Totalwork–Workdonebybothon4days.$

$WorkLeft=W-\frac{28W}{60}$

$LCM=60;$

$WorkLeft=\frac{(60W-28W)}{60}=\frac{32W}{60}=\frac{16W}{30}=\frac{8W}{15}$

Hence, $\frac{8}{15}$ is fraction of work left.