A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed in how many days will the project be completed?a)16 daysb)27 daysc)26.67 daysd)18 daysCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Given:
A can complete the project in 20 days
B can complete the project in 30 days

To find:
In how many days will the project be completed if A quits 10 days before it is completed?

Approach:
To solve this problem, we can calculate the rate at which A and B work individually and then find their combined rate when working together. Using their combined rate, we can determine the number of days required to complete the project.

Let's start by calculating the work rate of A and B separately.

Calculating the work rate of A:
A can complete the project in 20 days, which means that A completes 1/20th of the project in a day.
So, the work rate of A is 1/20.

Calculating the work rate of B:
B can complete the project in 30 days, which means that B completes 1/30th of the project in a day.
So, the work rate of B is 1/30.

Now, let's calculate their combined work rate when working together.

Calculating the combined work rate:
When A and B work together, their work rates are added.
Combined work rate = 1/20 + 1/30
Combining the fractions, we get 3/60 + 2/60 = 5/60.
So, the combined work rate is 5/60.

Now, let's determine the number of days required to complete the project.

Calculating the number of days:
Let the number of days required to complete the project when A quits be x.
Since A quits 10 days before the project is completed, A works for (x-10) days.
B works for x days.

Using the work rate formula (Work = Rate * Time), we can write the equation:

1 = (5/60) * (x-10) + (1/30) * x

Simplifying the equation:
Multiplying through by 60 to eliminate fractions, we get:

60 = 5(x-10) + 2x

60 = 5x - 50 + 2x

Combining like terms, we get:

60 = 7x - 50

Adding 50 to both sides, we get:

110 = 7x

Dividing by 7, we get:

x = 110/7

x ≈ 15.71

Therefore, the project will be completed in approximately 15.71 days, which can be rounded to 16 days.

Hence, the correct answer is option D) 16 days.

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