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41. 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?

42. A and B can do a work in 12 days, B and C in 15 days, C and A in 20 days. If A, B and C work together, they will complete the work in

AnswerAnswer: OptionC Explanation:

(A+B)' s 1 day's work = 1/12; (B+C)'s 1 day's work = 1/ 15; (A+ C)'s 1 day's work = 1/20. Adding, we get : 2 (A+B+C)'s 1 day's work = (1/12+1/15+1/20) = 12/60 = 1/5. therefore (A+B+C)'s 1 day's work = 1/10. so A,B and C together can complete the work in 10 days.

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43. A and B can do a piece of work in 72 days; B and C can do it in 120 days; A and C can do it in 90 days.In what time can A alone do it/

AnswerAnswer: OptionC Explanation:

(A+B)'s 1 day's work = 1/72; (B+C)'s 1 day's work = 1/120; (A+C)'s 1 day's work = 1/90. Adding, we get : 2 (A+B+C)'s 1 day's work = (1/72+1/120+1/90) = 12/360 = 1/30. = (A+B+C)'s 1 day's work = 1/60. so, A's 1 day's work = (1/60 - 1/120) = 1/120. therefore A alone can do the work in 120 days.

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44. A and B can do a piece of work in 5 days; B and C can do it in 7 days; A and C can do it in 4 days. who among these will take the least time if put to do it alone?

AnswerAnswer: OptionC Explanation:

(A+B)'s 1 day's work = 1/5; (B+C)'s 1 day's work = 1/7; (A+C)'s 1 day's work =1/4. Adding, we get : 2 (A + B + C) 's 1 day's work = (1/5 + 1/7 + 1/4) = 83/140. (A+B+C)'s 1 day's work = 83/280. A's 1 day's work = (83/280 - 1/7) = 43/280; B's 1 day's work = (83/280 - 1/4) = 13/280; C's 1 day's work = (83/280 - 1/5) =27/280. Thus time taken by A,B,C is 280/43 day's, 280/13 day's, 280/27 days respectively. Clearly, the time taken by A is least.

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45. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

AnswerAnswer: OptionA Explanation:

2(A+B+C)'s 1 day's work = (1/30+1/24+1/20) = 15/120 = 1/8. = (A+B+C)'s 1 day's work =1/16. Work done by A,B and C in 10 days = 10/16 = 5/8. Remaining work = (1- 5/8) = 3/8. A's 1 day's work = (1/16 - 1/24) = 1/48. Now, 1/48 work is done by A in 1 day. so, 3/8 work will be done by A in (48*3/8) = 18 days.

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