Question : A and B complete a work in 24 and 30 days, respectively, working 10 hours per day. The work is to be done in two shifts. The morning shift is for 6 hours and the evening shift is for 4 hours. On the first day, A works in the morning and B works in the evening, and they interchange their shifts every day. On which day did the work get completed?
Option 1: 21st day
Option 2: 24th day
Option 3: 30th day
Option 4: 27th day
Correct Answer: 27th day
Solution : Given: A can complete the whole work in 24 days. B can complete the whole work in 30 days. Now, Total work = LCM of 24 and 30 = 120 Efficiency of A = $\frac{120}{24}$ = 5 Efficiency of B = $\frac{120}{30}$ = 4 Since Work done by A and B in 10 hours of one day is 5 and 4 respectively. Work done by A and B in two days = 5 + 4 = 9 days A and B repeat the same process on all 26 days Work completed by A and B in 26 days = 9 × 13 =117 Remaining work = 120 – 117 = 3 Efficiency of A and B in 2 days = 5 + 4 = 9 so, 3 part work will be completed in = $\frac{2}{3}$ days The total time taken to complete the work = $26\tfrac{2}{3}$ days So, the total work is completed on the 27th day. Hence, the correct answer is the 27th day.
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Question : Working 7 hours a day, 18 persons can complete a certain work in 32 days. In how many days would 14 persons complete the same work, working 8 hours a day?
Option 1: 42
Option 2: 30
Option 3: 35
Option 4: 36
Question : Reena, Veena, and Vimla can do a work in 4 hours, 8 hours, and 12 hours, respectively. In how much time will they finish the work working together?
Option 1: $\frac{2}{11}$ hours
Option 2: $5\frac{2}{11}$ hours
Option 3: $3\frac{2}{11}$ hours
Option 4: $2\frac{2}{11}$ hours
Question : If 45 persons can complete a work in 18 days, working 8 hours a day, then how many persons are required to complete two-thirds of the same work in 20 days, working 9 hours a day?
Option 1: 36
Option 2: 40
Option 3: 30
Option 4: 24
Question : If 10 men can complete a piece of work in 12 days by working 7 hours a day, then in how many days can 14 men do the same work by working 6 hours a day?
Option 1: 15
Option 2: 16
Option 3: 10
Option 4: 12
Question : A and B working together can do a piece of work in $4\frac{1}{2}$ hours. B and C working together can do it in 3 hours. C and A working together can do it in $2\frac{1}{4}$ hours. All of them begin the work at the same time. Find how much time they will take to finish the piece of work.
Option 1: 3 hours
Option 2: 2 hours
Option 3: 2.5 hours
Option 4: 3.25 hours
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