Question : Sanjay and Rohan can complete a work in 8 days and 12 days, respectively. Starting with Sanjay, they work on alternate days. In how many days will the work be completed?
Option 1: $8 \frac{1}{2}$
Option 2: $9 \frac{1}{2}$
Option 3: $9 \frac{2}{3}$
Option 4: $9 \frac{1}{3}$
Correct Answer: $9 \frac{1}{2}$
Solution : Time taken by Sanjay to complete the work = 8 days Part of work done by Sanjay in a day = $\frac{1}{8}$ Time taken by Rohan to complete the work = 12 days Part of work done by Rohan in a day = $\frac{1}{12}$ Part of the work done by Sanjay and Rohan in two days = $\frac{1}{8}+\frac{1}{12}$ = $\frac{3+2}{24}$ = $\frac{5}{24}$ Part of the work done by Sanjay and Rohan in 8 days = $\frac{5×4}{24} = \frac{20}{24}$ Part of the work done by Sanjay in 9th day = $\frac{1}{8} = \frac{3}{24}$ Remaining work = $\frac{24-20-3}{24} = \frac{1}{24}$ Time taken by Rohan to complete the remaining work = $\frac{\frac{1}{24}}{\frac{1}{12}} = \frac{1}{2}$ day Total time taken = $9+\frac{1}{2}= 9\frac{1}{2}$ days Hence, the correct answer is $9\frac{1}{2}$.
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Question : A can complete a work in 8 days and B can complete the same work in 11 days. How many days will they take, if both work together?
Option 1: $4 \frac{12}{17}$
Option 2: $5 \frac{12}{19}$
Option 3: $4 \frac{11}{19}$
Option 4: $4 \frac{12}{19}$
Question : A can complete $\frac{2}{3}$ of a work in 4 days and B can complete $\frac{3}{5}$ of the work in 6 days. In how many days can both A and B together complete the work?
Option 1: $3$
Option 2: $2$
Option 3: $3\frac{3}{4}$
Option 4: $2\frac{7}{8}$
Question : A can do $\frac{2}{5}$ of a work in 6 days and B can do $\frac{2}{3}$ of the same work in 12 days. A and B worked together for 6 days. C alone completed the remaining work in 8 days. A and C, working together, will complete the same work in:
Option 1: 9 days
Option 2: 12 days
Option 3: 10 days
Option 4: 8 days
Question : A can do $\frac{2}{5}$ of a work in 12 days while B can do $66 \frac{2}{3}\%$ of the same work in 16 days. They work together for 10 days. B alone will complete the remaining work in:
Option 1: 6 days
Option 2: 4 days
Option 3: 8 days
Option 4: 9 days
Question : A, B, and C working separately can do a piece of work in 11 days, 20 days, and 55 days respectively. In how many days, the work will be completed if A is assisted by B and C on alternate days?
Option 1: 2 days
Option 2: 6 days
Option 3: 4 days
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