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A can do a piece of work in 30 days, B can do in 45 days and C can do same work alone in 60 days. If on the first day A worked alone and on the second day A and B worked together and on the third day A and C worked together. If they repeat the cycle as follows then in how many days total work can be completed?
- a)21 Days
- b)21 7/8 Days
- c)21 5/6 Days
- d)21 4/9 Days
- e)None
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A can do a piece of work in 30 days, B can do in 45 days and C can do ...
First day = 1/30
Second day = 1/30+1/45
Third day = 1/30+1/60
3 days work = 3/30+1/45+1/60 = 25/180
3*7 = 21 days work = 175/180
Now 1/36 work is left which can be completed by A alone
1/36*30 = 5/6
21+5/6 = 21 5/6 Days
Second day = 1/30+1/45
Third day = 1/30+1/60
3 days work = 3/30+1/45+1/60 = 25/180
3*7 = 21 days work = 175/180
Now 1/36 work is left which can be completed by A alone
1/36*30 = 5/6
21+5/6 = 21 5/6 Days
Most Upvoted Answer
A can do a piece of work in 30 days, B can do in 45 days and C can do ...
Given: A can do a piece of work in 30 days, B can do in 45 days and C can do the same work alone in 60 days.
Let the total work be 180 units (LCM of 30, 45 and 60).
On the first day, A alone does 6 units of work (180/30).
On the second day, A and B together do (6+4) 10 units of work (LCM of 30 and 45 is 90, and A does 3 units of work in 1 day while B does 2 units of work in 1 day. So, in 1 day they will do 5 units of work. So, in 2 days, they will do 10 units of work).
On the third day, A and C together do (6+3) 9 units of work (LCM of 30 and 60 is 60, and A does 1 unit of work in 1 day while C does 1/3 units of work in 1 day. So, in 1 day they will do 4/3 units of work. So, in 3 days, they will do 4 units of work).
So, in 3 days, they have done a total of 25 units of work (6+10+9).
To complete 180 units of work, they need 155 units more (180-25).
Let's calculate the next 3 days cycle:
On the fourth day, A alone does 6 units of work.
On the fifth day, A and B together do 10 units of work.
On the sixth day, A and C together do 9 units of work.
So, in 6 days, they have done a total of 50 units of work (25+6+10+9).
To complete 180 units of work, they need 130 units more (180-50).
Let's calculate the next 3 days cycle:
On the seventh day, A alone does 6 units of work.
On the eighth day, A and B together do 10 units of work.
On the ninth day, A and C together do 9 units of work.
So, in 9 days, they have done a total of 75 units of work (25+6+10+9+6+10+9).
To complete 180 units of work, they need 105 units more (180-75).
Let's calculate the next 3 days cycle:
On the tenth day, A alone does 6 units of work.
On the eleventh day, A and B together do 10 units of work.
On the twelfth day, A and C together do 9 units of work.
So, in 12 days, they have done a total of 100 units of work (25+6+10+9+6+10+9+6+10+9).
To complete 180 units of work, they need 80 units more (180-100).
Let's calculate the next 3 days cycle:
On the thirteenth day, A alone does 6 units of work.
On the fourteenth day, A and B together do 10 units of work.
On the fifteenth day, A and C together do 9 units of work.
So, in 15 days, they have done a total of 125
Let the total work be 180 units (LCM of 30, 45 and 60).
On the first day, A alone does 6 units of work (180/30).
On the second day, A and B together do (6+4) 10 units of work (LCM of 30 and 45 is 90, and A does 3 units of work in 1 day while B does 2 units of work in 1 day. So, in 1 day they will do 5 units of work. So, in 2 days, they will do 10 units of work).
On the third day, A and C together do (6+3) 9 units of work (LCM of 30 and 60 is 60, and A does 1 unit of work in 1 day while C does 1/3 units of work in 1 day. So, in 1 day they will do 4/3 units of work. So, in 3 days, they will do 4 units of work).
So, in 3 days, they have done a total of 25 units of work (6+10+9).
To complete 180 units of work, they need 155 units more (180-25).
Let's calculate the next 3 days cycle:
On the fourth day, A alone does 6 units of work.
On the fifth day, A and B together do 10 units of work.
On the sixth day, A and C together do 9 units of work.
So, in 6 days, they have done a total of 50 units of work (25+6+10+9).
To complete 180 units of work, they need 130 units more (180-50).
Let's calculate the next 3 days cycle:
On the seventh day, A alone does 6 units of work.
On the eighth day, A and B together do 10 units of work.
On the ninth day, A and C together do 9 units of work.
So, in 9 days, they have done a total of 75 units of work (25+6+10+9+6+10+9).
To complete 180 units of work, they need 105 units more (180-75).
Let's calculate the next 3 days cycle:
On the tenth day, A alone does 6 units of work.
On the eleventh day, A and B together do 10 units of work.
On the twelfth day, A and C together do 9 units of work.
So, in 12 days, they have done a total of 100 units of work (25+6+10+9+6+10+9+6+10+9).
To complete 180 units of work, they need 80 units more (180-100).
Let's calculate the next 3 days cycle:
On the thirteenth day, A alone does 6 units of work.
On the fourteenth day, A and B together do 10 units of work.
On the fifteenth day, A and C together do 9 units of work.
So, in 15 days, they have done a total of 125
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A can do a piece of work in 30 days, B can do in 45 days and C can do same work alone in 60 days. If on the first day A worked alone and on the second day A and B worked together and on the third day A and C worked together. If they repeat the cycle as follows then in how many days total work can be completed?a)21 Daysb)21 7/8 Daysc)21 5/6 Daysd)21 4/9 Dayse)NoneCorrect answer is option 'C'. Can you explain this answer?
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