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Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?
- a)56
- b)54
- c)36
- d)18
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Aman and Akbar together can do a work in 18 days. Both of them began t...
Let the total work be W units.
Amount of work done by Aman in one day = Am units
Amount of work done by Akbar in one day = Ak units
W = (Am + Ak) 18
Now this piece of work has been started, but both worked for only 4 days, after which Aman took over,
⇒ W = (Am + Ak) 4 + (Am) 42
⇒ (Am + Ak) 18 = (Am + Ak) 4 + (Am)42
⇒ (Am + Ak) 14 = (Am) 42
⇒ Am + Ak = 3 Am
⇒ Ak = 2 Am
Substituting the value of Ak in the very first equation, we have
W = (Am + 2 Am)18
⇒ W = 54 Am
Hence, Aman alone would have taken 54 days to complete the work.
Amount of work done by Aman in one day = Am units
Amount of work done by Akbar in one day = Ak units
W = (Am + Ak) 18
Now this piece of work has been started, but both worked for only 4 days, after which Aman took over,
⇒ W = (Am + Ak) 4 + (Am) 42
⇒ (Am + Ak) 18 = (Am + Ak) 4 + (Am)42
⇒ (Am + Ak) 14 = (Am) 42
⇒ Am + Ak = 3 Am
⇒ Ak = 2 Am
Substituting the value of Ak in the very first equation, we have
W = (Am + 2 Am)18
⇒ W = 54 Am
Hence, Aman alone would have taken 54 days to complete the work.
Most Upvoted Answer
Aman and Akbar together can do a work in 18 days. Both of them began t...
Given Information:
- Aman and Akbar can complete a work together in 18 days.
- Akbar fell ill after 4 days of starting the work.
- Aman completed the remaining work in 42 days.
Calculation:
Let's assume the total work to be done is represented by 'x'.
Work done by Aman and Akbar in 1 day:
Aman and Akbar together can complete the work in 18 days, so their combined work rate per day is 1/18 of the total work.
Work done by Aman and Akbar in 4 days:
In 4 days, Aman and Akbar would have completed 4 * (1/18) = 4/18 of the work, which is 2/9 of the total work.
Remaining work:
Since Akbar fell ill after 4 days, the remaining work is (1 - 2/9) = 7/9 of the total work.
Aman's work rate:
Aman completed the remaining work in 42 days, so his work rate per day is 1/42 of the total work.
Time taken by Aman to complete the whole work alone:
To find out how long Aman would take to complete the whole work alone, we set up the equation:
Aman's work rate + Akbar's work rate = Combined work rate
1/x + 1/18 = 1/42
Solving the equation, we get x = 54 days.
Therefore, Aman can complete the whole work alone in 54 days. Hence, the correct answer is option 'B'.
- Aman and Akbar can complete a work together in 18 days.
- Akbar fell ill after 4 days of starting the work.
- Aman completed the remaining work in 42 days.
Calculation:
Let's assume the total work to be done is represented by 'x'.
Work done by Aman and Akbar in 1 day:
Aman and Akbar together can complete the work in 18 days, so their combined work rate per day is 1/18 of the total work.
Work done by Aman and Akbar in 4 days:
In 4 days, Aman and Akbar would have completed 4 * (1/18) = 4/18 of the work, which is 2/9 of the total work.
Remaining work:
Since Akbar fell ill after 4 days, the remaining work is (1 - 2/9) = 7/9 of the total work.
Aman's work rate:
Aman completed the remaining work in 42 days, so his work rate per day is 1/42 of the total work.
Time taken by Aman to complete the whole work alone:
To find out how long Aman would take to complete the whole work alone, we set up the equation:
Aman's work rate + Akbar's work rate = Combined work rate
1/x + 1/18 = 1/42
Solving the equation, we get x = 54 days.
Therefore, Aman can complete the whole work alone in 54 days. Hence, the correct answer is option 'B'.
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Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?a)56b)54c)36d)18Correct answer is option 'B'. Can you explain this answer?
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Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?a)56b)54c)36d)18Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?a)56b)54c)36d)18Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?a)56b)54c)36d)18Correct answer is option 'B'. Can you explain this answer?.
Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?a)56b)54c)36d)18Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?a)56b)54c)36d)18Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Aman and Akbar together can do a work in 18 days. Both of them began to work. After 4 days Akbar fell ill, Aman completed the remaining work in 42 days. In how many days can Aman complete the whole work if he did it alone?a)56b)54c)36d)18Correct answer is option 'B'. Can you explain this answer?.
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