A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
📊 Work and Time Calculation 📊
A and B’s combined work rate = 1/8 (work done per day)
B and C’s combined work rate = 1/12 (work done per day)
A, B, and C’s combined work rate = 1/6 (work done per day)
Let’s find the combined work rate of A and C:
(A + B) + (B + C) – (A + B + C) = 1/8 + 1/12 – 1/6
Combine like terms:
(2B) – B = 1/8 + 1/12 – 1/6
B = 1/8 + 1/12 – 1/6
B’s work rate = (3 + 2 – 4) / 24
= 1/24
Now, find A’s work rate + C’s work rate:
A’s work rate + C’s work rate = (A, B, and C’s combined work rate) – B’s work rate
= 1/6 – 1/24
= (4 – 1) / 24
= 3/24
= 1/8
Time taken = 1 / (A’s work rate + C’s work rate)
= 1 / (1/8)
= 8 days
A and C together will do the work in 8 days.
