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?
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?
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The LCM method is generally the fastest way to solve Time \& Work problems as it avoids fractions and simplifies calculations.
Updated On: Jul 4, 2026
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Correct Answer: 8
Approach Solution - 1
Approach: Stop thinking in fractions. Assume the total work is the LCM of 12 and 18, so both rates become clean whole numbers \(-\) that is the fastest way to handle any "start together, one leaves" problem.
Step 1: Let the total work \(= \text{LCM}(12, 18) = 36\) units.
Step 2: Find the daily rates.
A does \(\frac{36}{12} = 3\) units/day, B does \(\frac{36}{18} = 2\) units/day.
Step 3: For the first 4 days both work together at \(3 + 2 = 5\) units/day.
\[ \text{Work done in 4 days} = 5 \times 4 = 20 \text{ units} \]
Step 4: A now leaves. Remaining work \(= 36 - 20 = 16\) units, and only B continues at 2 units/day.
\[ \text{Days for B} = \frac{16}{2} = 8 \text{ days} \]
Final Answer: B takes 8 more days.
Step 1: Let the total work \(= \text{LCM}(12, 18) = 36\) units.
Step 2: Find the daily rates.
A does \(\frac{36}{12} = 3\) units/day, B does \(\frac{36}{18} = 2\) units/day.
Step 3: For the first 4 days both work together at \(3 + 2 = 5\) units/day.
\[ \text{Work done in 4 days} = 5 \times 4 = 20 \text{ units} \]
Step 4: A now leaves. Remaining work \(= 36 - 20 = 16\) units, and only B continues at 2 units/day.
\[ \text{Days for B} = \frac{16}{2} = 8 \text{ days} \]
Final Answer: B takes 8 more days.
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Approach Solution -2
Total-work (LCM) method: Take the total work as \( 36 \) units (LCM of 12 and 18), so A's rate \( =36/12=3 \) units/day and B's rate \( =36/18=2 \) units/day.
Working together for \( 4 \) days, they complete \( 4\times(3+2)=20 \) units, leaving \( 36-20=16 \) units of work.
B alone does \( 2 \) units/day, so B needs \( 16/2=8 \) more days to finish the remaining work.
\[ \boxed{8 \text{ days}} \]
Working together for \( 4 \) days, they complete \( 4\times(3+2)=20 \) units, leaving \( 36-20=16 \) units of work.
B alone does \( 2 \) units/day, so B needs \( 16/2=8 \) more days to finish the remaining work.
\[ \boxed{8 \text{ days}} \]
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