Question:
A can do a work in 12 days and B in 18 days. if they start work together, and after 2 days B leaves then how many days will it take for the work to get completed?
A can do a work in 12 days and B in 18 days. if they start work together, and after 2 days B leaves then how many days will it take for the work to get completed?
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The LCM method is often faster and less prone to calculation errors than the fraction method for Time and Work problems.
Updated On: Dec 8, 2025
- 7
- 8.66
- 9
- 10.66
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
A and B work together for 2 days, after which B leaves. A completes the rest of the work alone. We need to find the total time taken to complete the entire work.
Step 2: Key Formula or Approach:
We will use the LCM method to find the total work and individual efficiencies. - Total Work = LCM of individual times. - Efficiency = Total Work / Time taken.
Step 3: Detailed Explanation:
Time taken by A = 12 days.
Time taken by B = 18 days.
Let the total work be the LCM of 12 and 18, which is 36 units.
- A's efficiency (work per day) = 36 / 12 = 3 units/day. - B's efficiency (work per day) = 36 / 18 = 2 units/day.
Combined efficiency of A and B = 3 + 2 = 5 units/day.
They work together for 2 days. Work done in 2 days = Combined efficiency \(\times\) 2 = 5 \(\times\) 2 = 10 units.
Remaining work = Total work - Work done = 36 - 10 = 26 units.
B leaves, and A completes the remaining 26 units of work alone.
Time taken by A to finish the remaining work = Remaining work / A's efficiency Time = 26 / 3 = 8.66 days.
The question asks for the total number of days for the work to get completed.
Total days = Days they worked together + Days A worked alone Total days = 2 + 8.66 = 10.66 days.
Step 4: Final Answer:
The total time taken for the work to get completed is 10.66 days.
A and B work together for 2 days, after which B leaves. A completes the rest of the work alone. We need to find the total time taken to complete the entire work.
Step 2: Key Formula or Approach:
We will use the LCM method to find the total work and individual efficiencies. - Total Work = LCM of individual times. - Efficiency = Total Work / Time taken.
Step 3: Detailed Explanation:
Time taken by A = 12 days.
Time taken by B = 18 days.
Let the total work be the LCM of 12 and 18, which is 36 units.
- A's efficiency (work per day) = 36 / 12 = 3 units/day. - B's efficiency (work per day) = 36 / 18 = 2 units/day.
Combined efficiency of A and B = 3 + 2 = 5 units/day.
They work together for 2 days. Work done in 2 days = Combined efficiency \(\times\) 2 = 5 \(\times\) 2 = 10 units.
Remaining work = Total work - Work done = 36 - 10 = 26 units.
B leaves, and A completes the remaining 26 units of work alone.
Time taken by A to finish the remaining work = Remaining work / A's efficiency Time = 26 / 3 = 8.66 days.
The question asks for the total number of days for the work to get completed.
Total days = Days they worked together + Days A worked alone Total days = 2 + 8.66 = 10.66 days.
Step 4: Final Answer:
The total time taken for the work to get completed is 10.66 days.
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