Question : A can do $\frac{1}{4}$th part of a work in 9 days. B can do $\frac{2}{3}$rd part of the same work in 28 days. Working together, in how many days can A and B complete the whole work?
Option 1: $\frac{262}{11}$ days
Option 2: $\frac{252}{13}$ days
Option 3: $\frac{261}{15}$ days
Option 4: $\frac{198}{17}$ days
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Correct Answer: $\frac{252}{13}$ days
Solution : Given: A can do $\frac{1}{4}$ part of a work in 9 days. A does the whole work in $9\times 4=36$ days. So, A's one day's work = $\frac{1}{36}$. B can do $\frac{2}{3}$ part of the same work in 28 days. B does the whole work in $28\times \frac{3}{2}=42$ days. So, B's one day's work = $\frac{1}{42}$. The number of days required by A and B to complete the whole work together = $\frac{1}{\frac{1}{36}+\frac{1}{42}}=\frac{1}{\frac{7+6}{252}}=\frac{252}{13}$ days Hence, the correct answer is $\frac{252}{13}$ days.
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Question : A and B can complete a piece of work in 13 and 17 days respectively. A begins to do the work, and they work alternatively one at a time for one day each. The whole work will be completed in:
Option 1: $17 \frac{11}{17}$ days
Option 2: $17 \frac{17}{19}$ days
Option 3: $14 \frac{11}{17}$ days
Option 4: $11 \frac{11}{17}$ days
Question : A can do $\frac{1}{3}$ of a work in 30 days. B can do $\frac{2}{5}$ of the same work in 24 days. They worked together for 20 days. C completed the remaining work in 8 days. Working together A, B and C will complete the same work in:
Option 1: 15 days
Option 2: 10 days
Option 3: 18 days
Option 4: 12 days
Question : P, Q, and R can complete a piece of work in 10 days, 15 days, and 20 days, respectively. If they work together, in how many days can they finish the same work?
Option 1: $4 \frac{8}{13}$
Option 2: $4 \frac{3}{7}$
Option 3: $4 \frac{7}{13}$
Option 4: $4 \frac{5}{7}$
Question : A and B can complete a work in 10 and 16 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in:
Option 1: $12 \frac{1}{4}$ days
Option 2: $13 \frac{1}{4}$ days
Option 3: $15 \frac{1}{4}$ days
Option 4: $14 \frac{1}{4}$ days
Question : A can do a piece of work in 6 days, working 8 hours a day, while B can do the same work in 4 days, working 10 hours a day. If the work has to be completed in 5 days, how many hours do they need to work together in a day?
Option 1: $4$
Option 2: $5\frac{4}{11}$
Option 3: $6\frac{4}{11}$
Option 4: $4\frac{4}{11}$
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