Question : A and B can do a piece of work in 5 days and 10 days, respectively. They began the work together but A left after some days and B finished the remaining work in 8 days. After how many days did A leave?
Option 1: $3\frac{1}{8}$
Option 2: $5\frac{1}{8}$
Option 3: $6\frac{1}{8}$
Option 4: $\frac{2}{3}$
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Correct Answer: $\frac{2}{3}$
Solution : Time taken by A alone to complete the work = 5 days Work done by A alone in a day = $\frac{1}{5}$ Time taken by B alone to complete the work = 10 days Work done by B alone in a day = $\frac{1}{10}$ Work done by B alone in 8 days = $\frac{8}{10}$ Work done by A and B together $= 1-\frac{8}{10}=\frac{2}{10}=\frac{1}{5}$ So they do $\frac{1}{5}$th part work in $\frac{\frac{1}{5}}{\frac{1}{5}+\frac{1}{10}}=\frac{1}{5}×\frac{10}{3}=\frac{2}{3}$ days Hence, the correct answer is $\frac{2}{3}$.
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Question : A, B, and C can separately do work in 6, 10, and 15 days respectively. They started to work together but C left after 2 days. In how many days will the remaining work be finished?
Option 1: $1 \frac{2}{4}$
Option 2: $1 \frac{1}{4}$
Option 3: $1 \frac{5}{8}$
Option 4: $2 \frac{7}{4}$
Question : A, B, and C can do a job in 6 days, 12 days and 15 days respectively. After $\frac{1}{8}$th of the work is completed, C leaves the job. The rest of the work is done by A and B together. The time taken to finish the work is:
Option 1: $5\frac{5}{6}$ days
Option 2: $5\frac{1}{4}$ days
Option 3: $3\frac{1}{2}$ days
Option 4: $3\frac{3}{4}$ days
Question : A, B, and C can separately complete a work in 12, 15, and 20 days, respectively. They worked together for 4 days. What will be the remaining work?
Option 1: $\frac{1}{2}$
Option 2: $\frac{1}{5}$
Option 3: $\frac{1}{6}$
Option 4: $\frac{1}{8}$
Question : A can do a piece of work in 9 days, while B can do it in 12 days. A and B together can do the work in:
Option 1: $5\frac{1}{7}$ days
Option 2: $5\frac{2}{7}$ days
Option 3: $6\frac{1}{7}$ days
Option 4: $6\frac{2}{7}$ days
Question : 10 women took 16 days to complete a work which can be completed by 6 men in 8 days. 12 men started working and after 2 days 6 men left and 5 women joined them. In how many days will the remaining work be completed?
Option 1: $\frac{3}{2}$
Option 2: $\frac{16}{5}$
Option 3: $\frac{5}{2}$
Option 4: $\frac{24}{5}$
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