


29.
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in: [S.S.C 2003]
Answer & Solution
Answer: c) 25 days
Solution: (A + B)'s 1 day's work = 1/10 C's 1 day's work = 1/50 (A + B + C)'s 1 day's work = (1/10 + 1/50) = 6/50 = 3/25 ....... (i) Also, A's 1 day's work = (B + C)'s 1 day's work .......(ii) From (i) and (ii), we get : 2 * (A's 1 day's work) = 3/25 => A's 1 day's work = 3/50 B's 1 day's work = (1/10  3/50) = 2/50 = 1/25 So, B alone could do the work in 25 days. 30.
A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is: [Asstt. Grade. 1997]
31.
A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in: [S.S.C. 1999]
Answer & Solution
Answer: b) 22 1/2 days
Solution: Ratio of times taken by A and B = 1 : 3. If difference of time is 2 days, B takes 3 days. If difference of time is 60 days, B takes [(3/2) * 60] = 90 days. So, A takes 30 days to do the work. A's 1 day's work = 1/30 B's 1 day's work = 1/90 (A + B)'s 1 day's work = (1/30 + 1/90) = 4/90 = 2/45 A and B together can do the work in 45/2 = 22 1/2 days. 32.
A and B can do a job together in 7 days. A is 1 3/4 times as efficient as B. The same job can be done by A alone in: [S.S.C. 2003]
33.
A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days? [Hotel Management 1998]
Answer & Solution
Answer: b) 13 days
Solution: Ratio of time taken by A and B = 100 : 130 = 10 : 13. Suppose B takes x days to do the work. Then, 10 : 13 :: 23 : x => x = [(23 * 13) /10] => x = 299/10 A's 1 day's work = 1/23 B's 1 day's workk = 10/299 (A + B)'s 1 day's work = [(1/23) + (10/299)] = 23/299 = 1/13 A and B together can complete the job in 13 days. 34.
A does half as much work as B in threefourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?
35.
A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 40 days, then A, B and C together can do the work in:
Answer & Solution
Answer: d) 13 1/3 days
Solution: (A's 1 day's work) : (B's 1 day's work) = 150 : 100 = 3 : 2. Let A's and B's 1 day's work be 3x and 2x respectively. Then, C's 1 day's work = [(3x + 2x)/2] = 5x/2 5x/2 = 1/40 or x = [(1/40) * (2/5)] = 1/100 A's 1 day's work = 3/100 B's 1 day's work = 1/50 C's 1 day's work = 1/40 (A + B + C)'s 1 day's work = [(3/100) + (1/50) + (1/40)] = 15/200 = 3/40 So, A, B and C together can do the work in 40/3 = 13 1/3 days 