A started a work and left after working for 2 days. Then B was called and he finished the work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them, working alone finish the whole work?Options2.5 days, 7.5 days5 days, 8.5 days5 days, 15 daysNone of these
Question
A started a work and left after working for 2 days. Then B was called and he finished the work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them, working alone finish the whole work?Options2.5 days, 7.5 days5 days, 8.5 days5 days, 15 daysNone of these
Solution
This problem can be solved using the concept of work and efficiency in time and work problems.
Step 1: Let's denote the total work to be done as 1 unit.
Step 2: From the problem, we know that A works for 2 days and B finishes the remaining work in 9 days. This can be written as: 2A + 9B = 1 ---- (equation 1)
Step 3: The problem also states that if A had worked for 3 days, B would have finished the remaining work in 6 days. This can be written as: 3A + 6B = 1 ---- (equation 2)
Step 4: Now, we have two equations with two variables. We can solve these equations to find the values of A and B.
Subtract equation 2 from equation 1, we get: -1A + 3B = 0 => A = 3B ---- (equation 3)
Step 5: Substitute equation 3 in equation 1, we get: 2(3B) + 9B = 1 => 15B = 1 => B = 1/15
Step 6: Substitute B = 1/15 in equation 3, we get: A = 3(1/15) = 1/5
So, A can finish the work in 5 days and B can finish the work in 15 days. Therefore, the answer is 5 days, 15 days.
Similar Questions
A and B together can finish a work in 6.75 days. A alone can finish the same work in 9 days. In how many days will B alone finish the work?Options18 days27 days35 days36 days
Select the correct answerA and B together can finish a work in 5 days. If A works twice his efficiency they can finish the same work in 3 days. In how many days will A alone finish the work?Options5.4 days7.5 days6.6 days15 days
A can do a piece of work in 8 days and B can do the same work in 10 days. They started the work together but after 3 days, A left . In how many days B can complete the remaining work?4 days7 days7.5 days3. 25 days
A started a work and left working after 9 days now B finished the remaining work in 24 days. Had A left the work after working for 13 days then B would have finished the remaining work in next 18 days. Then find in how many days A and B together can complete the work?Options12 days15 days16 days18 days
A can finish one-third of a work in 5 days, B can finish 2/5th of the same work in 10 days and C can finish 75% of the same work in 15 days. They work together for 6 days; The remaining work will be finished by B alone in?Options5 days3 days2.5 days1.5 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.