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A and B can complete a work in 15 days and 10 days, respectively. They started doing the work together but after 2 days, B had to leave and A alone completed the remaining work. The whole work was completed in
- a)10 days
- b)8 days
- c)12 days
- d)15 days
- e)None of the above
Correct answer is option 'C'. Can you explain this answer?
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A and B can complete a work in 15 days and 10 days, respectively. They...
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A and B can complete a work in 15 days and 10 days, respectively. They...
To solve the problem of A and B completing the work, we can break it down step by step.
Work Done by A and B
- A can complete the work in 15 days, so A's work rate is \( \frac{1}{15} \) of the work per day.
- B can complete the work in 10 days, so B's work rate is \( \frac{1}{10} \) of the work per day.
Combined Work Rate
- When A and B work together, their combined work rate is:
\[
\frac{1}{15} + \frac{1}{10} = \frac{2}{30} + \frac{3}{30} = \frac{5}{30} = \frac{1}{6}
\]
- Thus, together they complete \( \frac{1}{6} \) of the work in one day.
Work Done in First 2 Days
- In 2 days, the amount of work completed by A and B together is:
\[
2 \times \frac{1}{6} = \frac{2}{6} = \frac{1}{3}
\]
- Therefore, \( \frac{1}{3} \) of the work is done, leaving \( \frac{2}{3} \) of the work remaining.
Work Done by A Alone
- After 2 days, B leaves, and A continues to work alone.
- A's rate is \( \frac{1}{15} \) of the work per day.
- To complete the remaining \( \frac{2}{3} \) of the work, we calculate the number of days A needs:
\[
\text{Days required} = \left(\frac{2/3}{1/15}\right) = \frac{2/3 \times 15}{1} = 10 \text{ days}
\]
Total Time Taken
- The total time to complete the work is the initial 2 days plus the 10 days A worked alone:
\[
2 + 10 = 12 \text{ days}
\]
Thus, the entire work was completed in 12 days. The correct answer is option 'C'.
Work Done by A and B
- A can complete the work in 15 days, so A's work rate is \( \frac{1}{15} \) of the work per day.
- B can complete the work in 10 days, so B's work rate is \( \frac{1}{10} \) of the work per day.
Combined Work Rate
- When A and B work together, their combined work rate is:
\[
\frac{1}{15} + \frac{1}{10} = \frac{2}{30} + \frac{3}{30} = \frac{5}{30} = \frac{1}{6}
\]
- Thus, together they complete \( \frac{1}{6} \) of the work in one day.
Work Done in First 2 Days
- In 2 days, the amount of work completed by A and B together is:
\[
2 \times \frac{1}{6} = \frac{2}{6} = \frac{1}{3}
\]
- Therefore, \( \frac{1}{3} \) of the work is done, leaving \( \frac{2}{3} \) of the work remaining.
Work Done by A Alone
- After 2 days, B leaves, and A continues to work alone.
- A's rate is \( \frac{1}{15} \) of the work per day.
- To complete the remaining \( \frac{2}{3} \) of the work, we calculate the number of days A needs:
\[
\text{Days required} = \left(\frac{2/3}{1/15}\right) = \frac{2/3 \times 15}{1} = 10 \text{ days}
\]
Total Time Taken
- The total time to complete the work is the initial 2 days plus the 10 days A worked alone:
\[
2 + 10 = 12 \text{ days}
\]
Thus, the entire work was completed in 12 days. The correct answer is option 'C'.
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A and B can complete a work in 15 days and 10 days, respectively. They started doing the work together but after 2 days, B had to leave and A alone completed the remaining work. The whole work was completed in a)10 daysb)8 daysc)12 daysd)15 dayse)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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