


1.
Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take both A and B, working together but independently, to do the same job? [IGNOU 2003]
2.
A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? [Bank P.O. 2003]
3.
A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 2/5 hours a day?
Answer & Solution
Answer: b) 3 days
Solution: A can complete the work in (7 * 9) = 63 hours. B can complete the work in (6 * 7) = 42 hours. A's 1 hour's work = 1/63 B's 1 hour's work = 1/42 (A + B)'s 1 hour's work = (1/63 + 1/42) = 5/126 Both will finish the work in (126/5) hrs. Number of days of 8 2/5 hrs each = (126/5 * 5/42) = 3 days. 4.
A and B can do a piece of work in 18 days, B and C can do it in 24 days; A and C can do it in 36 days. In how many days will A, B and C finish it, working together and separately?
Answer & Solution
Answer: d) 144 days
Solution: (A + B)'s 1 day's work = 1/18 (B + C)'s 1 day's work = 1/24 (A + C)'s 1 day's work = 1/36 Adding, we get: 2 (A + B + C)'s 1 day's work = (1/18 + 1/24 + 1/36) = 9/72 = 1/8 (A + B + C)'s 1 day's work = 1/16. Thus, A, B and C together can finish the work in 16 days. Now, A's 1 day's work = [(A + B + C)'s 1 day's work]  [(B + C)'s 1 day's work] = (1/16  1/24) = 1/48. A alone can finish the work in 48 days. Similarly, B's 1 day's work = (1/16  1/36) = 5/144 B alone can finish the work in 144/5 = 28 4/5 days C's 1 day's work = (1/16  1/18) = 1/144 C alone can finish the work in 144 days. 5.
A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?
6.
A can do a certain job in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
7.
A can do a piece of work in 80 days. He works at 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?
Answer & Solution
Answer: b) 30 days
Solution: Work done by A in 10 days = [(1/80) * 10] = 1/8 Remaining work = [1  (1/8)] = 7/8 Now, 7/8 work is done by B in 42 days. Whole work will be done by B in [42 * (8/7)] = 48 days. A's 1 day's work = 1/80 and B's 1 day's work = 1/48 (A + B)'s 1 day's work = (1/80 + 1/48) = 8/240 = 1/30 Hence, both will finish the work in 30 days. 