A and B can do a piece of work in 20 days, B and C can do it in 60 days. If B alone can do it in 90 days, in how many days will A and C do it together?
Question
A and B can do a piece of work in 20 days, B and C can do it in 60 days. If B alone can do it in 90 days, in how many days will A and C do it together?
Solution
Sure, let's solve this step by step:
Step 1: Find the work done by A and B together in one day. Since A and B can complete the work in 20 days, they can do 1/20 of the work in one day.
Step 2: Similarly, find the work done by B and C together in one day. Since B and C can complete the work in 60 days, they can do 1/60 of the work in one day.
Step 3: Find the work done by B alone in one day. Since B can complete the work in 90 days, B can do 1/90 of the work in one day.
Step 4: Now, we know that (work done by A and B in one day) + (work done by B and C in one day) = (work done by A, B, and C in one day) + 2*(work done by B in one day).
So, 1/20 + 1/60 = (work done by A, B, and C in one day) + 2*(1/90).
Solving this equation gives us the work done by A, B, and C in one day as 1/15.
Step 5: We know that (work done by A, B, and C in one day) = (work done by A and C in one day) + (work done by B in one day).
So, 1/15 = (work done by A and C in one day) + 1/90.
Solving this equation gives us the work done by A and C in one day as 1/18.
Step 6: Therefore, A and C together can complete the work in 18 days.
Similar Questions
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if B and C assist him on every third day?
A can do a piece of work in 5 days and B in 20 days. They work together for 2 days and then both leave the work. Then C alone can finish the remaining work in 6 days. In how many days will C finish the full work?
A can do a piece of work in 80 days. He works on it for 10 days and then B alone finishes the remaining work in 42 days. In how much time will A and B working together, finish the work?A 40 days B 30 days C 60 days D 50 days
9) A & B can do a piece of work in 72 days, B & C can do it in 120 days and A & C can do in in 90 days. In how many days all three together can do the work?
A and B together can complete a piece of work in 35 days, while A alone can complete it in 60 days. So, B alone can complete the work in how many days?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.