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6. 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?

AnswerAnswer: OptionB Explanation:

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.

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7. 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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8. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m and the remaining two machines complete the work. Approximately at what time will the work be finished?

AnswerAnswer: OptionD Explanation:

(P+Q+R)'s 1 hour's work = (1/8+1/10+1/12) = 37/120. Work done by P, Q and R in 2 hours = (37/120*2) = 37/60. Remaining work = (1- 37/60) = 23/60. (Q+R)'s 1 hour's work = (1/10+ 1/12) = 11/60. Now, 11/60 work is done by Q and R in 1 hour. So, 23/60 work will be done by Q and R in (60/11*23/60) = 23/11 hours = 2 hours. So, the work will be finished approximately 2 hours after 11 a.m., i.e., around 1p.m.

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9. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?

AnswerAnswer: OptionC Explanation:

(B+C)'s 1 day's work = ( 1/9 + 1/12) = 7/36. work done by B and C in 3 days = (7/36*3) = 7/12. Remaining work = (1- 7/12) = 5/12. Now, 1/24 work is done by A in 1 day. so, 5/12 work is done by A in (24*5/12) = 10 days.

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10. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. the whole work was completed in?

AnswerAnswer: OptionD Explanation:

(A+B)'s 1 day's work = (1/15+ 1/10) = 1/6. work done by A and B in 2 days = (1/6*2) = 1/3. Remaining work = ( 1- 1/3) = 2/3. Now, 1/15 work is done by A in 1 day. therefore 2/3 work will be done by A in (15*2/3) = 10 days. hence, total time taken = (10+2) = 12 days.

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