If A takes half as long to do a piece of work as B takes and if C does it in the same time as A and B together and if all three working together would take 7 days, then how long would each take separately?Marks : 2Negative Marks : 0Answer here21, 42, 1414, 35, 2114, 42, 4942, 35, 49
Question
If A takes half as long to do a piece of work as B takes and if C does it in the same time as A and B together and if all three working together would take 7 days, then how long would each take separately?Marks : 2Negative Marks : 0Answer here21, 42, 1414, 35, 2114, 42, 4942, 35, 49
Solution
Let's denote the amount of work as W.
-
If A takes half as long to do a piece of work as B takes, then A does twice as much work in the same time as B. So, if B does W in b days, A does W in a = b/2 days.
-
If C does it in the same time as A and B together, then C does W in c = a + b days.
-
If all three working together would take 7 days, then 1/a + 1/b + 1/c = 1/7.
Substituting a = b/2 and c = a + b into the equation, we get 2/b + 1/b + 1/(b + 2b/2) = 1/7, which simplifies to 3/b + 1/(3b/2) = 1/7.
Solving this equation for b, we get b = 14 days. Then a = b/2 = 7 days and c = a + b = 21 days.
So, A would take 7 days, B would take 14 days, and C would take 21 days to do the work separately.
Similar Questions
A can do a piece of work in 4 hours. B and C can do the same piece of work together in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?Marks : 1Negative Marks : 0Answer here12638
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 task in 10 days, while B and C together can complete the same task in 15 days. If A, B, and C work together, how long will it take to complete the task?A) 5 days B) 6 days C) 7.5 days D) 8 days
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:4 days6 days8 days12 days
A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all the three, working together can complete the job in 24 days, then the number of days. A alone will take to finish the job is
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.