In 75% of the time that B takes to do a piece of work, A does half the work. Together they take 18 days to complete the work. C alone can complete the same work in 24 days. All the three started the work together but B left 5 days before the completion of the work. In how many days was the whole work completed?
Answers
Answer:
30 days
Step-by-step explanation:
Let B takes x days to do the work.
According to the question
A takes 2×
4
3x
=
2
3x
(A+B)s 1 days work=
18
1
then
x
1
+
3x
2
=
18
1
3x
5
=
18
1
x=
3
18×5
=30
Hence B takes 30 days to do work
Answer:
The whole work was completed in 28 days.
Step-by-step explanation:
Let's assume time taken by A, B, and be a, b, and c, respectively.
From the problem, we know that:
In 75% of the time it takes for B to do the work, A does half the work.
(3/4)B × (1/2)A = 1 (1 represents the whole work)
Simplifying the equation, we get:
A = (8/3)b
Together, A, B, and C take 18 days to complete the work.
1/a + 1/b + 1/c = 1/18
Work done by C alone in 24 days.
c = 1/24
Let's substitute the value of A in terms of B into the equation we got for A and B working together:
1/a + 1/b + 1/c = 1/18
1/[(8/3)b] + 1/b + 24 = 1/18
Simplifying the equation, we get:
b = 36/7
Now we can find the value of A:
A = (8/3) * (36/7) = 96/7
So, the combined rate of A and B working together is:
1/a + 1/b = 7/96
Now let's consider the scenario where A, B, and C start working together but B leaves 5 days before the completion of the work.
Let's assume that the whole work is completed in d days. This means that B worked for (d-5) days and A and C worked for d days.
Let's use the combined rate formula again, but this time we'll use (d-5) for the time B worked:
1/a + 1/b = 7/96
1/a + 1/b + 1/c = 1/18
1/a + 1/c = 1/((d-5)/b)
Substituting the values we know, we get:
1/(96/7) + 1/(36/7) = 7/96
1/(96/7) + 1/(36/7) + 1/24 = 1/18
1/(96/7) + 1/24 = 1/((d-5)/(36/7))
Simplifying the equations, we get:
d = 28
Therefore, the whole work was completed in 28 days.
To know more about work concept, click on the link below:
https://brainly.in/question/15114333
To know more about rate formula, click on the link below:
https://brainly.in/question/49353677
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