27. A and B together can do a piece of work in 15 days; B and C together can do it in 12 days;
Cand A can do it in 20 days. How long will they take to finish the work, working together?
Also find the number of days taken by each to do the same work, working alone
Best Answer and hand written solution will be marked as brainliest answer
Answers
Answer:
A&B=20
B&C=15
C&A=12
According to L.C.M of 20,15,12
we get 60.
That means
A & B can do 3 units of work in 1 day.(A+B= 3)
B & C can do 4 units of work in 1 day.(B+C=4)
C & A can do 5 units of work in 1 day.(C+A=5)
3+4+5 =12
2(A + B+ C) = 12
A+B+C =6
(A+B)+C=6
3+C=6
C=3 per day
C can do 3 units of work per day,So In How many days it will take to complete 60 units of work??
DAYS ————— ———1 (?)
Total units of work——-3 (60)
(60/3)*1=20
C=20 days
A+B+C =6
A+(B+C)=6
A+4=6
A=2 per day
A can do 2 units of work per day,So In How many days it will take to complete 60 units of work??
DAYS ————— ———1 (?)
Total units of work——-2(60)
(60/2)*1=30
A=30 days
A+B+C=6
B+(C+A)=6
B+5=6
B=1 per day
B can do 1 unit of work per day,So In How many days it will take to complete 60 units of work??
DAYS ————— ———1 (?)
Total units of work——-1(60)
(60/1)*1=60
B=60 days
A can take 30 days
B can take 60 days
C can take 20 days to complete the work.
Answer:
All 3 can complete the work together in 10 days.
A needs 60 days to complete the work alone.
B needs 20 days to complete the work alone.
C needs 30 days to complete the work alone.
Step-by-step explanation:
Hii mate ^_^
A and B = 15 days
B and C = 12 days
C and A = 20 days
LCM(15,12,20)=60
Now this 60 units can be treated as the total work and we will now calculate the one day work
One day work of A and B = 60/15 = 4 units
One day work of B and C = 60/12 = 5 units
One day work of C and A = 60/20= 3 units
Now if we add all three we get:-
2(A+B+C)=12 units
So one day work of A, B and C put together is 12/2 = 6 units
If the total work is of 60 units and the one day work of A , B and C is 6 unit
So,
No. of days for completing the work together = 60/6 = 10 days
Hence,
All 3 can complete the work together in 10 days.
To find one day work of A :-
One day work of A, B and C together minus one day work of B and C, that is 6–5 = 1 units
If the total work is of 60 units and the one day work of A is 1 unit, then alone A needs 60/1 = 60 days to finish the work.
Hence,
A needs 60 days to complete the work alone.
To find one day work of B :-
One day work of A, B and C together minus one day work of C and A, that is 6–3 = 3 units
If the total work is of 60 units and the one day work of B is 3 unit, then alone B needs 60/3 = 20 days to finish the work.
Hence,
B needs 20 days to complete the work alone.
To find one day work of C :-
One day work of A, B and C together minus one day work of A and B, that is 6–4 = 2 units
If the total work is of 60 units and the one day work of C is 2 units , then alone C needs 60/2 = 30 days to finish the work.
Hence,
C needs 30 days to complete the work alone.