Question : Akshita and Raina are typing a book, but have only one laptop to work on. They decided that they would work on an alternate basis such that Akshita would work for the first day, Raina would work for the second day, Akshita for the third day and so on. Akshita alone can finish the typing work in 16 days, while Raina will take 24 days if she works alone on the entire book. How many days will they take to finish the typing work if they work on an alternate basis?
Option 1: 15
Option 2: 18
Option 3: 19
Option 4: 17
Correct Answer: 19
Solution : Time taken by Akshita to complete the work = 16 days Part of work done by Akshita in a day = $\frac{1}{16}$ Time taken by Raina to complete the work = 24 days Part of work done by Raina in a day = $\frac{1}{24}$ Part of the work done by Akshita and Raina in 2 days = $\frac{1}{16}+\frac{1}{24}=\frac{3+2}{48}=\frac{5}{48}$ Part of the work done by Akshita and Raina in 18 days =$ \frac{5×9}{48}=\frac{45}{48}$ Remaining work = $\frac{48-45}{48} = \frac{3}{48} = \frac{1}{16}$ Time taken by Raina to complete the remaining work = $\frac{\frac{1}{16}}{\frac{1}{16}}=1$ day Total time taken = 18 + 1 = 19 days Hence, the correct answer is 19.
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Question : A group of workers can complete a piece of work in 50 days when they are working individually. On the first day one person works, on the second day, another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many approximate days are needed to complete the work?
Option 1: 8 days
Option 2: 9 days
Option 3: 10 days
Option 4: 11 days
Question : A can do work in 12 days and B in 24 days. If they work together, in how many days will they finish the work?
Option 1: 12 days
Option 2: 20 days
Option 3: 15 days
Option 4: 8 days
Question : A can do work in 12 days and B in 20 days. If they together work on it for 5 days and the remaining work is completed by C in 3 days, then in how many days can C do the same work alone?
Option 1: 10 days
Option 3: 12 days
Option 4: 15 days
Question : A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively. How soon can the work be done if A works with B on the first day, A works with C on the second day and so on?
Option 1: $8 \frac{1}{2}$ days
Option 2: $9\frac{1}{2}$ days
Option 3: 8 days
Option 4: 9 days
Question : Tapas works twice as fast as Mihir. If both of them together complete a work in 12 days, Tapas alone can complete it in:
Option 1: 15 days
Option 2: 18 days
Option 3: 20 days
Option 4: 24 days
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