Question

A can do a piece of work in 9 days working 8 hours per day and B can do it in 6 days working 9 hours per day. If they will work together for 9 hours a day, then they will complete the work in

• A. 5 days
• B. 7 days
• C. $7\frac{2}{3}\text{days}$
• D. $3\frac{3}{7}\text{days}$

Answer 1

The correct option is D $3\frac{3}{7}\text{days}$

A can complete the whole work in $=9\times 8=72$ hours
A's 1 hour work $=\frac{1}{72}$
B can complete the whole work in $=6\times 9=54$ hours
$\Rightarrow$ B's 1 hour work $=\frac{1}{54}$
(A+B)’s 1 hour work $=\frac{1}{72}+\frac{1}{54}=\frac{3+4}{216}=\frac{7}{216}$
$\Rightarrow$ Both will finish the work in $=\frac{216}{7}$ hours
$\Rightarrow$ Number of days required to finish the whole work, working together for 9 hours $=\frac{216}{7}\times \frac{1}{9}=\frac{24}{7}=3\frac{3}{7}\text{days}$
Option (c) is correct.