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P is four times as efficient as Q.P can complete a work in 45 days less than Q. If both of them work together, then in how many days the work will be completed?
- a)10
- b)12
- c)15
- d)30
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
P is four times as efficient as Q.P can complete a work in 45 days les...
Let P completes the work in x days
as P is 4 times efficient than q ; q takes 4x days to complete the work
now 4x - x = 45
3x = 45
x = 15 days
so p takes 15 days to complete the work
and q takes 4x days i.e. 4x15 = 60 days
now both can complete the work in one day
= 1/15 + 1/60 = 75 / 15 x 60
= 1/12 work
So total 12 days required to complete the work.
Most Upvoted Answer
P is four times as efficient as Q.P can complete a work in 45 days les...
To solve this problem, let's assume that Q takes x days to complete the work.
Given that P is four times as efficient as Q, we can say that P takes 1/4th of the time taken by Q to complete the work. So, the time taken by P is x/4 days.
We are also given that P can complete the work in 45 days less than Q. This can be expressed as:
x = (x/4) - 45
Simplifying this equation, we get:
4x = x - 180
3x = -180
x = -60
Since time cannot be negative, this solution is not valid.
Therefore, there must be a mistake in the given information. It is not possible for P to be four times as efficient as Q and also complete the work in 45 days less than Q.
As a result, we cannot determine the number of days it will take for them to complete the work together. The correct answer cannot be determined based on the given information.
Given that P is four times as efficient as Q, we can say that P takes 1/4th of the time taken by Q to complete the work. So, the time taken by P is x/4 days.
We are also given that P can complete the work in 45 days less than Q. This can be expressed as:
x = (x/4) - 45
Simplifying this equation, we get:
4x = x - 180
3x = -180
x = -60
Since time cannot be negative, this solution is not valid.
Therefore, there must be a mistake in the given information. It is not possible for P to be four times as efficient as Q and also complete the work in 45 days less than Q.
As a result, we cannot determine the number of days it will take for them to complete the work together. The correct answer cannot be determined based on the given information.
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