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If 10 persons can do a job in 20 days, then 20 person with twice the efficiency can do the same job in:
- a)5 days
- b)40 days
- c)10 days
- d)20 days
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If 10 persons can do a job in 20 days, then 20 person with twice the e...
M x D = 10 x 20 = 200
Man-days New Man-days = (20 x 2) x x
► 200 = 20 x 2 x x
► x = 5 days
or M1D1 = M2D2
► 10 x 20 = (20 x 2) x x
► ⇒ x = 5
Man-days New Man-days = (20 x 2) x x
► 200 = 20 x 2 x x
► x = 5 days
or M1D1 = M2D2
► 10 x 20 = (20 x 2) x x
► ⇒ x = 5
Most Upvoted Answer
If 10 persons can do a job in 20 days, then 20 person with twice the e...
Given:
- 10 persons can do a job in 20 days.
To find:
- How long will it take for 20 persons with twice the efficiency to do the same job?
Solution:
Let's assume that the amount of work to be done is W.
If 10 persons can do the job in 20 days, then the work done by each person in one day is W/10.
Now, let's consider the work done by 20 persons with twice the efficiency in one day. Each person will now do the work at a rate of 2(W/10), which can be simplified as W/5.
Therefore, the work done by 20 persons in one day is W/5.
Since the amount of work to be done remains the same, we can set up the following equation:
Work done by 10 persons in 20 days = Work done by 20 persons in x days
(W/10) * 20 = (W/5) * x
Simplifying the equation, we get:
20 = 2x
x = 10 days
Conclusion:
- If 10 persons can do a job in 20 days, then 20 persons with twice the efficiency can do the same job in 10 days. Therefore, the correct answer is option 'C' - 10 days.
- 10 persons can do a job in 20 days.
To find:
- How long will it take for 20 persons with twice the efficiency to do the same job?
Solution:
Let's assume that the amount of work to be done is W.
If 10 persons can do the job in 20 days, then the work done by each person in one day is W/10.
Now, let's consider the work done by 20 persons with twice the efficiency in one day. Each person will now do the work at a rate of 2(W/10), which can be simplified as W/5.
Therefore, the work done by 20 persons in one day is W/5.
Since the amount of work to be done remains the same, we can set up the following equation:
Work done by 10 persons in 20 days = Work done by 20 persons in x days
(W/10) * 20 = (W/5) * x
Simplifying the equation, we get:
20 = 2x
x = 10 days
Conclusion:
- If 10 persons can do a job in 20 days, then 20 persons with twice the efficiency can do the same job in 10 days. Therefore, the correct answer is option 'C' - 10 days.
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