Question

A can do a piece of work in 9 days and B in 18 days. They began the work together but 3 days before the completion of work A leaves. The time taken to complete the work is:
A. 7 days
B. 5 days
C. 8 days
D. 11 days

Answer 1

Hint: Here the question describes the speed of two member to complete the work and then want to calculate the time taken to complete the work when both start work together but one member leave the work before 3 days of completion, here we have to go through the unit day work conversion which means first we have to calculate the speed of both the member for 1 day work and then solve.

Complete step-by-step answer:
The given question need to solve for the work done by two members when they work together at their speed but one member left the work before 3 days of completion, here we have to first find the individual day work then we have to solve further for the work left and they work together, on solving we get:
 Work done by A in 1 day = \[ \dfrac{1}{9} \]
 Work done by B in 1 day = \[ \dfrac{1}{{18}} \]
 Work done by B in last 3 days = \[\dfrac{1}{{18}} \times 3 = \dfrac{1}{6} \]
 Remaining work = \[ 1 - \dfrac{1}{6} = \dfrac{5}{6} \]
Work done by A and B in 1 day = \[ \dfrac{1}{9} + \dfrac{1}{{18}} = \dfrac{3}{{18}} = \dfrac{1}{6} \]
Hence number of days in which A and B worked together is
\[\dfrac{{\dfrac{5}{6}}}{{\dfrac{1}{6}}} = 5 \] days
Then total time to complete the work = 3 + 5 = 8 days
Hence the total time taken to complete the work is 8 Days.
So, the correct answer is “Option C”.

Note: Here to solve this question the best optimum way is to use unit work per day conversion, and after simplification we can reach to the total time taken to complete the same work, what they complete alone in their respective days, and after simplification we can find the time taken.