A and B together can do a piece of work in 15 days, B and C together can do it in 12 days, A and C can do it in 20 days. How long will they take to finish the work together?
Answers
Answer:
- They will take 10 days to finish the work together.
Step-by-step explanation:
To Find:
- How long will they take to finish the work together?
Find the time taken to finish the work together:
A and B together can do a piece of work in 15 days.
- (A + B)'s one day work = 1/15 ____(i)
B and C together can do it in 12 days.
- (B + C)'s one day work = 1/12 ____(ii)
A and C can do it in 20 days.
- (A + C)'s one day work = 1/20 ____(iii)
Adding eqⁿ(i), eqⁿ(ii) and eqⁿ(iii).
(A + B) + (B + C) + (A + C) = 1/15 + 1/12 + 1/20
A + B + B + C + A + C = (4 + 5 + 3)/60
2A + 2B + 2C = 12/60
2(A + B + C) = 1/5
(A + B + C) = 1/(5 × 2)
(A + B + C) = 1/10
Here,
- (A + B + C)'s one day work = 1/10
- So, A, B and C together can finish the work in 10 days.
Answer:
Given :-
A and B together can do a piece of work in 15 days, B and C together can do it in 12 days, A and C can do it in 20 days.
To Find :-
How long will they take to finish the work together?
Solution :-
At first
We have
A + B = 15
B + C = 12
A + C = 20
Work done in 1 day
A + B = 1/15
B + C = 1/12
A + C = 1/20
When they do work together
(A + B) + (B + C) + (A + C) = (1/15) + (1/12) + (1/20)
A + B + B + C + A + C = 1/15 + 1/12 + 1/20
2A + 2B + 2C = 1(4) + 1(5) + 1(3)/60
2A + 2B + 2C = 4 + 5 + 3/60
2(A + B + C) = 12/60
2(A + B + C) = ⅕
2(A + B + C)/2 = ⅕/2
A + B + C = ⅕ × ½
A + B + C = 1/10.
Work done by A + B + C in one day = 1/10
Total days taken = 10 days