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A can do a piece of work in 82 days, B can do in 123 days and C can do the same work alone in 164 days. If on the first day A worked alone and on the second day B and C worked together and on the third day A and C worked together. If they repeat the cycle, then in how many days total work can be completed?
- a)68(2/7)
- b)63(2/7)
- c)67(2/7)
- d)65(2/7)
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A can do a piece of work in 82 days, B can do in 123 days and C can d...
Given:
A can do a piece of work in 82 days
B can do a piece of work in 123 days
C can do a piece of work in 164 days
Approach:
Let the total work be 492 units (LCM of 82, 123, and 164).
Find the work done by each person in a day.
Calculate the work done in each cycle of three days.
Find the total number of cycles required to complete the work.
Multiply the number of cycles by 3 to get the total number of days required to complete the work.
Calculation:
Let the total work be 492 units.
A can do 6 units of work in a day (492/82).
B can do 4 units of work in a day (492/123).
C can do 3 units of work in a day (492/164).
On the first day, A does 6 units of work.
On the second day, B and C together do (4+3) = 7 units of work.
On the third day, A and C together do (6+3) = 9 units of work.
So, in each cycle of three days, they do 6+7+9 = 22 units of work.
The total number of cycles required to complete 492 units of work = 492/22 = 22 (rounded off to the nearest integer).
Therefore, the total number of days required to complete the work = 22 x 3 = 66 days.
Answer: Option (C) 67(2/7)
A can do a piece of work in 82 days
B can do a piece of work in 123 days
C can do a piece of work in 164 days
Approach:
Let the total work be 492 units (LCM of 82, 123, and 164).
Find the work done by each person in a day.
Calculate the work done in each cycle of three days.
Find the total number of cycles required to complete the work.
Multiply the number of cycles by 3 to get the total number of days required to complete the work.
Calculation:
Let the total work be 492 units.
A can do 6 units of work in a day (492/82).
B can do 4 units of work in a day (492/123).
C can do 3 units of work in a day (492/164).
On the first day, A does 6 units of work.
On the second day, B and C together do (4+3) = 7 units of work.
On the third day, A and C together do (6+3) = 9 units of work.
So, in each cycle of three days, they do 6+7+9 = 22 units of work.
The total number of cycles required to complete 492 units of work = 492/22 = 22 (rounded off to the nearest integer).
Therefore, the total number of days required to complete the work = 22 x 3 = 66 days.
Answer: Option (C) 67(2/7)
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Community Answer
A can do a piece of work in 82 days, B can do in 123 days and C can d...
Given :
Time taken by A to complete a work = 82 days
Time taken by B to complete a work = 123 days
Time taken by C to complete a work = 164 days
Concept used :
Total work = efficiency x Time taken
Calculation :
Let the total taken be 492 units
The efficiency of A = 492 / 82 = 6 units
The efficiency of B = 492 / 123 = 4 units
The efficiency of C = 492 / 164 = 3 units
Total work of A on the first day = 6 units
Total work of B and C on the second day = 7 units
Total work of A and C on the third day = 9 units
Total work in three days = 22 units
Total work in 67 days = 22 x 22 + 6 = 490 units
Work remaining for 68th day = 2 units
B and C together work on the 68th day
So, The total work is completed in 67(2/7)
∴ The answer is 67(2/7).
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A can do a piece of work in 82 days, B can do in 123 days and C can do the same work alone in 164 days. If on the first day A worked alone and on the second day B and C worked together and on the third day A and C worked together. If they repeat the cycle, then in how many days total work can be completed?a)68(2/7)b)63(2/7)c)67(2/7)d)65(2/7)Correct answer is option 'C'. Can you explain this answer?
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