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P can do a piece of work in 20 days. Q is 25 percent more efficient than P. In how many days half the work is completed when both are working simultaneously?
- a)41/9
- b)40/9
- c)39/9
- d)43/9
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
P can do a piece of work in 20 days. Q is 25 percent more efficient th...
Q is 25 percent more efficient so he will complete the work in 16 days
(1/20 + 1/16)*t = 1/2
(1/20 + 1/16)*t = 1/2
Most Upvoted Answer
P can do a piece of work in 20 days. Q is 25 percent more efficient th...
Given:
P can do a piece of work in 20 days.
Q is 25% more efficient than P.
To find:
In how many days half the work is completed when both are working simultaneously.
Solution:
Let the total work to be done be 100 units.
So, P can do 5 units of work in a day.
Q is 25% more efficient than P, so Q can do 25/100 * 5 = 1.25 units of work in a day.
Therefore, both P and Q working together can do 5 + 1.25 = 6.25 units of work in a day.
Let the number of days taken to complete half the work be x.
So, in x days, P and Q working together will complete 6.25x units of work.
According to the question, 6.25x = 50
Hence, x = 50/6.25 = 8
Therefore, the answer is 8 days.
Shortcut:
Alternatively, we can use the formula:
Number of days = Total work / Work done per day
For half the work to be completed, the total work to be done is 100/2 = 50 units.
P can do 5 units of work in a day, and Q can do 1.25 units of work in a day.
So, the work done per day by both P and Q working together is 5 + 1.25 = 6.25 units.
Therefore, the number of days taken to complete half the work is 50/6.25 = 8 days.
Hence, the answer is option B) 40/9.
P can do a piece of work in 20 days.
Q is 25% more efficient than P.
To find:
In how many days half the work is completed when both are working simultaneously.
Solution:
Let the total work to be done be 100 units.
So, P can do 5 units of work in a day.
Q is 25% more efficient than P, so Q can do 25/100 * 5 = 1.25 units of work in a day.
Therefore, both P and Q working together can do 5 + 1.25 = 6.25 units of work in a day.
Let the number of days taken to complete half the work be x.
So, in x days, P and Q working together will complete 6.25x units of work.
According to the question, 6.25x = 50
Hence, x = 50/6.25 = 8
Therefore, the answer is 8 days.
Shortcut:
Alternatively, we can use the formula:
Number of days = Total work / Work done per day
For half the work to be completed, the total work to be done is 100/2 = 50 units.
P can do 5 units of work in a day, and Q can do 1.25 units of work in a day.
So, the work done per day by both P and Q working together is 5 + 1.25 = 6.25 units.
Therefore, the number of days taken to complete half the work is 50/6.25 = 8 days.
Hence, the answer is option B) 40/9.
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P can do a piece of work in 20 days. Q is 25 percent more efficient th...
According to me , correct answer is option (E)
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