Question

$A$ can do a work in $15$ days and $B$ in $20$ days. If they work on it together for $4$ days, then the fraction of the work that is left is:

• A. $\frac{1}{4}$
• B. $\frac{1}{10}$
• C. $\frac{7}{15}$
• D. $\frac{8}{15}$

Answer 1

The correct option is D $\frac{8}{15}$

$A$'s $1$ day's work $=\frac{1}{15}$;

$B$'s $1$ day's work $=\frac{1}{20}$;

$(A+B)$'s $1$ day's work$=(\frac{1}{15}+\frac{1}{20})=\frac{7}{60}$

$(A+B)$'s $4$ day's work$=(\frac{7}{60}\times 4)=\frac{7}{15}$

Therefore, Remaining work $=(1-\frac{7}{15})=\frac{8}{15}$