Question

A, B, C can do a piece of work individually in $8,10$ and $15$ days respectively. A and B start working by A quits after working for $2$ days. After this, C joins B till the completion of work. In how many days will the work be completed?

• A. $53/9days$
• B. $34/7days$
• C. $85/13days$
• D. $53/10days$

Answer 1

The correct option is D $53/10days$

Work done by A in $1day=\frac{1}{8}$
Work done by B in $1day=\frac{1}{10}$
Work done by C in $1day=\frac{1}{15}$
Work done by A and B together in $1day=\frac{1}{8}+\frac{1}{10}$
$=\frac{5+4}{40}=\frac{9}{40}$
$\therefore$ In $2$ days A and B complete $2\times \frac{9}{40}=\frac{9}{20}$ of work
Work remaining $=1-\frac{9}{20}=\frac{11}{20}$
Work done by B and C together in $1day$
$=\frac{1}{10}+\frac{1}{15}$
$=\frac{3+2}{30}=\frac{5}{30}=\frac{1}{6}$
Let no. of days be n.
$\therefore n\times \frac{1}{6}=\frac{11}{20}$
$n=\frac{11}{20}\times 6=\frac{33}{10}days$
Total no. of days $=(2+\frac{33}{10})=\frac{53}{10}$