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Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.
- a)120 hrs
- b)40 hrs
- c)90 hrs
- d)15 hrs
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Three people are working on a project. Together, they take 10 hours t...
Let's assume that the total work in the project is represented by 'W'.
First, let's find the work done by A, B, and C individually:
- A completes one-third of the project, so the work done by A is (1/3)W.
- After A leaves, B and C together complete the remaining two-thirds of the project in 5 hours. So, their combined work rate is (2/5)W per hour.
- C takes 20 hours to complete the remaining part of the project, which is one-third of the total work. So, the work done by C is (1/3)W.
Now, let's calculate the total work done by A, B, and C together:
Since A completes one-third of the project, the work done by A is (1/3)W.
After A leaves, B and C together complete the remaining two-thirds of the project in 5 hours. So, their combined work rate is (2/5)W per hour. Therefore, the work done by B and C together in 5 hours is (2/5)*(2/3)W = (4/15)W.
We know that A, B, and C together take 10 hours to complete the project.
So, the equation becomes:
(1/3)W + (4/15)W + (1/3)W = W
Simplifying the equation, we get:
5/15W + 4/15W + 5/15W = W
14/15W = W
Multiplying both sides by 15, we get:
14W = 15W
W = 14
Therefore, the total work in the project is 14 units.
Now, let's calculate the time taken to complete the project if only B had been working on it:
Since B alone completes two-thirds of the project in 5 hours, we can set up the equation as follows:
(2/3)*14 = (2/5)*B*t
Simplifying the equation, we get:
28 = (2/5)*B*t
Multiplying both sides by 5/2, we get:
B*t = 28*(5/2)
B*t = 70
Since B is working alone, the time taken to complete the project is 't' hours. Therefore, we can rewrite the equation as:
B = 70/t
So, the time taken to complete the project if only B had been working on it is equal to 70 divided by the rate of work of B, which is 't' hours.
Option A, 120 hours, is the correct answer.
First, let's find the work done by A, B, and C individually:
- A completes one-third of the project, so the work done by A is (1/3)W.
- After A leaves, B and C together complete the remaining two-thirds of the project in 5 hours. So, their combined work rate is (2/5)W per hour.
- C takes 20 hours to complete the remaining part of the project, which is one-third of the total work. So, the work done by C is (1/3)W.
Now, let's calculate the total work done by A, B, and C together:
Since A completes one-third of the project, the work done by A is (1/3)W.
After A leaves, B and C together complete the remaining two-thirds of the project in 5 hours. So, their combined work rate is (2/5)W per hour. Therefore, the work done by B and C together in 5 hours is (2/5)*(2/3)W = (4/15)W.
We know that A, B, and C together take 10 hours to complete the project.
So, the equation becomes:
(1/3)W + (4/15)W + (1/3)W = W
Simplifying the equation, we get:
5/15W + 4/15W + 5/15W = W
14/15W = W
Multiplying both sides by 15, we get:
14W = 15W
W = 14
Therefore, the total work in the project is 14 units.
Now, let's calculate the time taken to complete the project if only B had been working on it:
Since B alone completes two-thirds of the project in 5 hours, we can set up the equation as follows:
(2/3)*14 = (2/5)*B*t
Simplifying the equation, we get:
28 = (2/5)*B*t
Multiplying both sides by 5/2, we get:
B*t = 28*(5/2)
B*t = 70
Since B is working alone, the time taken to complete the project is 't' hours. Therefore, we can rewrite the equation as:
B = 70/t
So, the time taken to complete the project if only B had been working on it is equal to 70 divided by the rate of work of B, which is 't' hours.
Option A, 120 hours, is the correct answer.
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Community Answer
Three people are working on a project. Together, they take 10 hours t...
Let the work per hour of A, B and C be a, b and c respectively.
Total work that needs to be done = 10(a+b+c). After 5 hours, work remaining = 5(a+b+c) which is done by c in 20 hours.
Therefore, 5(a+b+c) = 20c -> (1)
Since A completed one-third of the project by working for 5 hrs, we have 5a = (10/3)*(a+b+c) -> (2).
From (1) and (2), we get, a = 8b and c = 3b.
Therefore, total work involved in the project = 10*12b = 120b. Working alone, B takes 120 hours to finish it.
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Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer?
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