Question

Raja can do a piece of work in 14 days, while Rani can do the same work in 21 days. They started the work together but 3 days before the completion of the work, Raja left the work. The total number of days required to complete the work is :

• A. 7
• B. 8.5
• C. 5
• D. $10\frac{1}{5}$

Answer 1

The correct option is D $10\frac{1}{5}$

'3 days before the competion of the work Raja left the work' means in last 3 days only Rani has worked alone.
So, in last 3 days worked done by Rani $=3\times \frac{1}{21}=\frac{1}{7}$
So, the rest $(1-\frac{1}{7})=\frac{6}{7}$ work was done by Raja and Rani both.
Number of days in which Raja and Rani worked together
$=\frac{\frac{6}{7}}{\frac{5}{42}}=\frac{36}{5}=7\frac{1}{5}days$
Total number of days taken = 7.2 + 3 = 10.2 days

Note: Work done by Raja and Rani in one day $=\frac{1}{14}+\frac{1}{21}=\frac{5}{42}$
$(Also,numberofdays=\frac{Totalworktobedone}{Worktobedoneinoneday})$