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P does half as much work as Q in three-fourth of the time. If together they take 24 days to complete the work, how much time shall P take to complete the work?
- a)50 days
- b)60 days
- c)70 days
- d)80 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
P does half as much work as Q in three-fourth of the time. If together...
Let Q take x days to complete the work, so P will take 2*3/4 of X day to complete the work i.e. 3x/2 days
1/x + 2/3x = 1/24, we get x = 40 days, so P will take = 3/2 of 40 = 60 days
1/x + 2/3x = 1/24, we get x = 40 days, so P will take = 3/2 of 40 = 60 days
Most Upvoted Answer
P does half as much work as Q in three-fourth of the time. If together...
Let's assume that Q takes x days to complete the work. Therefore, P will take 2x days to complete the same work.
Given that P does half as much work as Q in three-fourth of the time, we can calculate the work efficiency ratio between P and Q.
Work efficiency ratio = (Work done by P) / (Work done by Q)
According to the given information,
Work done by P = 1/2
Work done by Q = 1
Therefore, the work efficiency ratio is (1/2) / 1 = 1/2.
Let's say the total work is represented by W.
- P does half as much work as Q, so the work done by P is (1/2)W.
- P takes 2x days to complete the work, so the work done by P in one day is (1/2)W / (2x) = W / (4x).
- Q takes x days to complete the work, so the work done by Q in one day is W / x.
Since P does half as much work as Q in three-fourth of the time, we can set up the following equation:
(1/2)(W / (4x)) = (3/4)(W / x)
Simplifying this equation, we get:
1 / (8x) = 3 / (4x)
Cross-multiplying, we get:
4x = 24x
Simplifying further, we get:
x = 6
Therefore, Q takes 6 days to complete the work.
Now, to find the time taken by P to complete the work, we can substitute the value of x back into the equation:
P takes 2x days = 2 * 6 = 12 days.
Hence, P takes 12 days to complete the work.
Therefore, the correct answer is option B) 60 days.
Given that P does half as much work as Q in three-fourth of the time, we can calculate the work efficiency ratio between P and Q.
Work efficiency ratio = (Work done by P) / (Work done by Q)
According to the given information,
Work done by P = 1/2
Work done by Q = 1
Therefore, the work efficiency ratio is (1/2) / 1 = 1/2.
Let's say the total work is represented by W.
- P does half as much work as Q, so the work done by P is (1/2)W.
- P takes 2x days to complete the work, so the work done by P in one day is (1/2)W / (2x) = W / (4x).
- Q takes x days to complete the work, so the work done by Q in one day is W / x.
Since P does half as much work as Q in three-fourth of the time, we can set up the following equation:
(1/2)(W / (4x)) = (3/4)(W / x)
Simplifying this equation, we get:
1 / (8x) = 3 / (4x)
Cross-multiplying, we get:
4x = 24x
Simplifying further, we get:
x = 6
Therefore, Q takes 6 days to complete the work.
Now, to find the time taken by P to complete the work, we can substitute the value of x back into the equation:
P takes 2x days = 2 * 6 = 12 days.
Hence, P takes 12 days to complete the work.
Therefore, the correct answer is option B) 60 days.
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