


43.
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last? [Bank P.O. 2004]
Answer & Solution
Answer: b) 10 days
Solution: Work done by X in 4 days = [(1/20) * 4] = 1/5. Remaining work = [1  (1/5)] = 4/5 (X + Y)'s 1 day's work = [1/20 + 1/12] = 8/60 = 2/15. Now, 2/15 work is done by X and Y in 1 day. So, 4/5 work will be done by X and Y in [(15/2) * (4/5)] = 6 days. Hence, total time taken = (6 + 4) days = 10 days. 44.
A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days, A alone can finish the job? [S.S.C. 2003]
45.
X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work? [Hotel Management 1999]
Answer & Solution
Answer: b) 13 1/3 days
Solution: Work done by X in 8 days = [1/40) * 8] = 1/5. Remaining work = [1  (1/5)] = 4/5. Now, 4/5 work is done by Y in 16 days. Whole work will be done by Y in [16 * (5/4)] = 20 days. X's 1 day's work = 1/40 Y's 1 day's work = 1/20 (X + Y)'s 1 day's work = [1/40 + 1/20] = 3/40. Hence, X and Y will together complete the work in 40/3 = 13 1/3 days. 46.
A, B and C together can complete a piece of work in 10 days. All the three started working at it together and after 4 days A left. Then B and C together completed the work in 10 more days. A alone could complete the work in:
Answer & Solution
Answer: c) 25 days
Solution: Work done by A, B and C in 4 days = [(1/10) * 4] = 2/5. Remaining work = [1  (2/5)] = 3/5 Now, 3/5 work is done by B and C in 10 days. Whole work will be done by B and C in [10 * 5/3] = 50/3 days. (A + B + C)'s 1 day's work = 1/10 (B + C)'s 1 day's work = 3/50 A's 1 day's work = [1/10)  (3/50)] = 2/50 = 1/25. A alone could complete the work in 25 days. 47.
A does 4/5 of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work? [S.S.C 2002]
Answer & Solution
Answer: c) 37 1/2 days
Solution: Whole work is done by A in [20 * (5/4)] = 25 days. Now, [1  (4/5)] i.e., 1/5 work is done by A and B in 3 days. Whole work will be done by A and B in (3 * 5) = 15 days. A's 1 day's work = 1/25. (A + B)'s 1 day's work = 1/15. B's 1 day's work = [1/15  1/25] = 4/150 = 2/75. So, B alone would do the work in 75/2 = 37 1/2 days. 48.
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone? [C.B.I. 1997]
49.
A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days C alone will do the work?
Answer & Solution
Answer: b) 24 days
Solution: A's 5 day's work + B's 7 day's work + C's 13 day's work = 1 => (A + B)'s 5 day's work + (B + C)'s 2 day's work + C's 11 day's work = 1 => 5/12 + 2/16 + C's 11 day's work = 1 => C's 11 day's work = 1  (5/12 + 2/16) = 11/24 => C's 1 day's work = [(11/24) * (1/11)] = 1/24 C alone can finish the work in 24 days. 