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A and B can together finish a work in 30 days. They worked for it for 20 days and then B left. The remaining work done by A alone in 20 more days. A alone can finish the work in
- a)48 days
- b)50 days
- c)54 days
- d)60 days
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A and B can together finish a work in 30 days. They worked for it for ...
Amount of work done in 1 day = 1/30
Amount of work done in 20 days = 20 * (1/30) = 2/3
Remaining work = 1 - 2/3 = 1/3
Given, A completes 1/3 work in 20 days.
Therefore, A can finish the whole work in (20 x 3) = 60 days.
HENCE OPTION D IS THE ANSWER
Amount of work done in 20 days = 20 * (1/30) = 2/3
Remaining work = 1 - 2/3 = 1/3
Given, A completes 1/3 work in 20 days.
Therefore, A can finish the whole work in (20 x 3) = 60 days.
HENCE OPTION D IS THE ANSWER
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Community Answer
A and B can together finish a work in 30 days. They worked for it for ...
Given Data:
- A and B can finish a work together in 30 days
- B left after working for 20 days
- A completed the remaining work in 20 more days
- A alone can finish the work in X days
Calculation:
Let's assume A's efficiency is \( x \) and B's efficiency is \( y \).
Efficiency Calculation:
- Together, A and B can complete the work in 30 days.
- So, their combined efficiency is \(\frac{1}{30}\) of the work per day.
Efficiency Equation:
\[ x + y = \frac{1}{30} \]
Work Done by A and B in 20 days:
- In 20 days, A and B completed \(20 \times (x + y) \) work.
Remaining work:
- The remaining work is \(1 - 20 \times (x + y) \).
Work done by A alone in 20 more days:
- A completed the remaining work in 20 days working alone.
- So, A's efficiency is \( x = \frac{1 - 20 \times (x + y)}{20} \).
Solving the Equations:
Plugging in the value of \( y \) in the efficiency equation:
\[ x + \frac{1}{30} - x = \frac{1}{30} \]
\[ \frac{1}{30} = \frac{1}{30} \]
So, A's efficiency is \( x = \frac{1}{60} \), which means A alone can finish the work in 60 days.
Therefore, the correct answer is option 'D'.
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