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A is twice as fast as B, and B is one third as fast as C. If they together can complete work in 30 days. In how many days, A, B and C individually can do the same work?
- a)60, 180, 240
- b)60, 180, 90
- c)180, 90, 60
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A is twice as fast as B, and B is one third as fast as C. If they tog...
Condition 1- A is twice as fast as
B means their ratio is 2: 1.
Condition 2- B is one third as fast
as C, means their ratio is 1: 3. Then we can say, the ratio of A, B and C is as follows
According to condition 1,
A : B = 2 : 1
According to condition 2;
B : C = 1 : 3
Thus, the ratio of A: B: C = 2: 1 : 3
This ratio denotes the working efficiency of A, B and C which means;
A, B and C can do = (2 + 1 + 3 = 6) work/day
Now we can calculate total work i.e.
Total work = Total days × Per day work
Total work = 30 × 6 = 180
A can do the same work in;
= (Total work / Efficiency of A) = 180 / 2 = 90 days
B can do the same work in;
= (Total work / Efficiency of B)
180 / 1 = 180 days
C can do the same work in;
= (Total work / Efficiency of C) = 180 / 3 = 60 days
Thus, A, B and C can individually complete the same work in 90, 180 and 60 days, respectively.
Most Upvoted Answer
A is twice as fast as B, and B is one third as fast as C. If they tog...
Let's assume that the work is to complete a task, such as painting a room or building a wall. We are given three individuals: A, B, and C. Our goal is to find out how long it would take for each individual to complete the task individually.
Given Information:
- A is twice as fast as B
- B is one third as fast as C
- A, B, and C together can complete the work in 30 days.
Step 1: Determine the Speed of B and C
Let's assume that B takes x days to complete the task.
Since A is twice as fast as B, A would take half the time, which is x/2 days.
Since B is one third as fast as C, C would take three times the time B takes, which is 3x days.
Step 2: Calculate the Proportion of Work Done
In 30 days, A, B, and C together complete the entire task. This means that the proportion of work done by each individual is as follows:
- A completes 1/30th of the work per day
- B completes 1/30th of the work per day
- C completes 1/30th of the work per day
Step 3: Calculate the Work Done by A, B, and C in a Day
Since A takes x/2 days to complete the task individually, the amount of work done by A in a day is 1/(x/2) = 2/x.
Since B takes x days to complete the task individually, the amount of work done by B in a day is 1/x.
Since C takes 3x days to complete the task individually, the amount of work done by C in a day is 1/(3x).
Step 4: Calculate the Proportion of Work Done by A, B, and C in a Day
We know that A completes 1/30th of the work in a day, so we can equate the proportion of work done by A in a day to 1/30:
2/x = 1/30
Solving for x, we get x = 60.
Step 5: Calculate the Work Done by A, B, and C Individually
Using the value of x, we can calculate the work done by A, B, and C individually:
A takes x/2 = 60/2 = 30 days
B takes x = 60 days
C takes 3x = 3*60 = 180 days
Therefore, the correct answer is option 'D' - None of these.
A takes 30 days, B takes 60 days, and C takes 180 days to complete the work individually.
Given Information:
- A is twice as fast as B
- B is one third as fast as C
- A, B, and C together can complete the work in 30 days.
Step 1: Determine the Speed of B and C
Let's assume that B takes x days to complete the task.
Since A is twice as fast as B, A would take half the time, which is x/2 days.
Since B is one third as fast as C, C would take three times the time B takes, which is 3x days.
Step 2: Calculate the Proportion of Work Done
In 30 days, A, B, and C together complete the entire task. This means that the proportion of work done by each individual is as follows:
- A completes 1/30th of the work per day
- B completes 1/30th of the work per day
- C completes 1/30th of the work per day
Step 3: Calculate the Work Done by A, B, and C in a Day
Since A takes x/2 days to complete the task individually, the amount of work done by A in a day is 1/(x/2) = 2/x.
Since B takes x days to complete the task individually, the amount of work done by B in a day is 1/x.
Since C takes 3x days to complete the task individually, the amount of work done by C in a day is 1/(3x).
Step 4: Calculate the Proportion of Work Done by A, B, and C in a Day
We know that A completes 1/30th of the work in a day, so we can equate the proportion of work done by A in a day to 1/30:
2/x = 1/30
Solving for x, we get x = 60.
Step 5: Calculate the Work Done by A, B, and C Individually
Using the value of x, we can calculate the work done by A, B, and C individually:
A takes x/2 = 60/2 = 30 days
B takes x = 60 days
C takes 3x = 3*60 = 180 days
Therefore, the correct answer is option 'D' - None of these.
A takes 30 days, B takes 60 days, and C takes 180 days to complete the work individually.
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A is twice as fast as B, and B is one third as fast as C. If they together can complete work in 30 days. In how many days, A, B and C individually can do the same work?a)60, 180, 240b)60, 180, 90c)180, 90, 60d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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