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

Answer: (D)

Let the total work be x units

Speed of A$=\frac{x}{15}$ work per day

Speed of B$=\frac{x}{20}$ work per day

$\therefore$ Speed of $A+B=\frac{7x}{60}$ work per day

Hence, if $A+B$ work together for 4 days then,

The amount of work they will complete will be $=\frac{7x}{60}\times 4=\frac{7x}{15}$ work

Now fraction of work left $=\frac{(x-\frac{7x}{15})}{x}=\frac{8}{15}$