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A and B together can complete some work in 24 days. If A, B and C work together, they can complete the same work in 18 days. B and C both have the same efficiency.
Q. A, B and C start working together from the very first day. If C leaves after 6 days and D (whose efficiency is equal to A) joins the work at that instant, then approximately how many days will be required to complete the work?
Correct answer is '16'. Can you explain this answer?
Verified Answer
A and B together can complete some work in 24 days. If A, B and C work...
We know that, A, B and C require 36, 72 and 72 days respectively to complete the work when working alone.
From the solution to the previous question, total work = 72 units and the efficiency of A, B and C (in units/day) is 2, 1 and 1 respectively.Since the efficiency of D is the same as that of A, d = 2 units/day as well.
A, B and C work together for the first 6 days.
So, amount of work done in the first 6 days = 6(a + b + c) = 6(2 + 1 + 1) = 24 units.
Now, C leaves and D joins the work.
So, the remaining 48 units of work is done by A, B and D.
Let the number of days taken by these three people by x.
So, 48 = (2 + 1 + 2) * x
x = 48/5 = 9.6 days
Since the work is incomplete at the end of day 9, the number of days taken has to be considered as 10.
So, total time taken to complete the work = 6 + 10 =16
Answer: 16
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
A and B together can complete some work in 24 days. If A, B and C work...
Given Information:
- A and B together can complete some work in 24 days.
- A, B, and C together can complete the same work in 18 days.
- B and C have the same efficiency.
Approach:
To solve this problem, we can break it down into smaller parts and calculate the work done by each person in a day. Let's assume that A's efficiency is a, B's efficiency is b, and C's efficiency is c.
Calculating Efficiency:
From the given information, we can form the following equations:
- (Equation 1) A + B = 1/24 (as A and B together can complete the work in 24 days)
- (Equation 2) A + B + C = 1/18 (as A, B, and C together can complete the work in 18 days)
Subtracting Equation 1 from Equation 2, we get:
- C = 1/18 - 1/24 = 1/72
Since B and C have the same efficiency, we can assume B's efficiency as b and C's efficiency as c. Therefore, we have:
- b + c = 1/72 (Equation 3)
Calculating Time:
Now let's calculate the time required to complete the work when A, B, and C start working together from the very first day and C leaves after 6 days, and D joins at that instant.
In 6 days, A, B, and C together complete 6 * (A + B + C) = 6 * (1/18) = 1/3 of the work.
After C leaves, B and D continue to work together. Since B and D have the same efficiency, we can assume D's efficiency as a. Therefore, we have:
- b + a = 1/24 (as A and B together can complete the work in 24 days)
Now, let's calculate the time required to complete the remaining 2/3 of the work when B and D work together:
- 2/3 = (b + a) * t (where t is the time required to complete the remaining work)
Solving this equation, we get:
- t = (2/3) / (b + a) = (2/3) / (1/24) = 16
Therefore, approximately 16 days will be required to complete the work when C leaves after 6 days and D joins at that instant.
- A and B together can complete some work in 24 days.
- A, B, and C together can complete the same work in 18 days.
- B and C have the same efficiency.
Approach:
To solve this problem, we can break it down into smaller parts and calculate the work done by each person in a day. Let's assume that A's efficiency is a, B's efficiency is b, and C's efficiency is c.
Calculating Efficiency:
From the given information, we can form the following equations:
- (Equation 1) A + B = 1/24 (as A and B together can complete the work in 24 days)
- (Equation 2) A + B + C = 1/18 (as A, B, and C together can complete the work in 18 days)
Subtracting Equation 1 from Equation 2, we get:
- C = 1/18 - 1/24 = 1/72
Since B and C have the same efficiency, we can assume B's efficiency as b and C's efficiency as c. Therefore, we have:
- b + c = 1/72 (Equation 3)
Calculating Time:
Now let's calculate the time required to complete the work when A, B, and C start working together from the very first day and C leaves after 6 days, and D joins at that instant.
In 6 days, A, B, and C together complete 6 * (A + B + C) = 6 * (1/18) = 1/3 of the work.
After C leaves, B and D continue to work together. Since B and D have the same efficiency, we can assume D's efficiency as a. Therefore, we have:
- b + a = 1/24 (as A and B together can complete the work in 24 days)
Now, let's calculate the time required to complete the remaining 2/3 of the work when B and D work together:
- 2/3 = (b + a) * t (where t is the time required to complete the remaining work)
Solving this equation, we get:
- t = (2/3) / (b + a) = (2/3) / (1/24) = 16
Therefore, approximately 16 days will be required to complete the work when C leaves after 6 days and D joins at that instant.
Community Answer
A and B together can complete some work in 24 days. If A, B and C work...
15.6 is also the correct answer
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A and B together can complete some work in 24 days. If A, B and C work together, they can complete the same work in 18 days. B and C both have the same efficiency.Q.A, B and C start working together from the very first day. If C leaves after 6 days and D (whose efficiency is equal to A) joins the work at that instant, then approximately how many days will be required to complete the work?Correct answer is '16'. Can you explain this answer?
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A and B together can complete some work in 24 days. If A, B and C work together, they can complete the same work in 18 days. B and C both have the same efficiency.Q.A, B and C start working together from the very first day. If C leaves after 6 days and D (whose efficiency is equal to A) joins the work at that instant, then approximately how many days will be required to complete the work?Correct answer is '16'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A and B together can complete some work in 24 days. If A, B and C work together, they can complete the same work in 18 days. B and C both have the same efficiency.Q.A, B and C start working together from the very first day. If C leaves after 6 days and D (whose efficiency is equal to A) joins the work at that instant, then approximately how many days will be required to complete the work?Correct answer is '16'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B together can complete some work in 24 days. If A, B and C work together, they can complete the same work in 18 days. B and C both have the same efficiency.Q.A, B and C start working together from the very first day. If C leaves after 6 days and D (whose efficiency is equal to A) joins the work at that instant, then approximately how many days will be required to complete the work?Correct answer is '16'. Can you explain this answer?.
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