Question

A, B and C can alone complete a work in 10, 12 and 15 days respectively. A and C started the work and after working for 4 days, A left and B joined. In how many days the total work was completed?

• A. $6\frac{5}{9}days$
• B. $6\frac{2}{9}days$
• C. $6days$
• D. $5\frac{4}{9}days$
• E. $7\frac{2}{9}days$

Answer 1

The correct option is B $6\frac{2}{9}days$

$(A+C)=\frac{1}{10}+\frac{1}{15}=\frac{1}{6}$. They worked for 4 days so did
$\frac{1}{6}\times 4=\frac{2}{3}=\frac{2}{3}rd$ of work
Remaining work =$1-\frac{2}{3}=\frac{1}{3}$
Now A left, B and C working
$(B+C)=(\frac{1}{12}+\frac{1}{15})=\frac{9}{60}=\frac{3}{20}$. They worked for x
days and completed $\frac{1}{3}rd$ of work so $\frac{3}{20}\times x=\frac{1}{3}$, so $x=\frac{20}{9}$days
Total =$4+\frac{20}{9}$