Question

A and B can complete a work in 12 days and 18 days respectively. They start together, but A leaves after 4 days. How many more days will B take to finish the remaining work?

Hint:

The LCM method is generally the fastest way to solve Time \& Work problems as it avoids fractions and simplifies calculations.

Answer 1

Correct Answer: 8

Step 1: A's rate \( =\frac{1}{12} \) of the work per day, B's rate \( =\frac{1}{18} \) per day, so together \( \frac{1}{12}+\frac{1}{18}=\frac{3+2}{36}=\frac{5}{36} \) per day.
Step 2: In 4 days together, work done \( =4\times\frac{5}{36}=\frac{20}{36}=\frac{5}{9} \). Remaining work \( =1-\frac{5}{9}=\frac{4}{9} \).
Step 3: B alone completes \( \frac{1}{18} \) per day, so time needed \( =\frac{4/9}{1/18}=\frac{4}{9}\times18=8 \).
\[ \boxed{8 \text{ days}} \]