Question : A can complete a task in 25 days while B can complete the same task in 30 days. They work on alternate days, starting with A. Both A and B follow this pattern for 5 days and then, A leaves. In how many days will B finish the remaining work?
Option 1: $24 \frac{2}{5}$
Option 2: $5 \frac{2}{5}$
Option 3: $5 \frac{3}{5}$
Option 4: $24 \frac{3}{5}$
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Correct Answer: $24 \frac{2}{5}$
Solution : A can complete the task in 25 days. Work done by A in one day = $\frac{1}{25}$ B can complete the task in 30 days. Work done by B in one day = $\frac{1}{30}$ They work on alternate days for 5 days. In 5 days, A worked for 3 days and B worked for 2 days. Work done in 5 days = $\frac{3}{25} + \frac{2}{30} = \frac{28}{150}$ After 5 days, A leaves, and B continues. The remaining work = $ 1 - \frac{28}{150} = \frac{122}{150}$ If B can do $\frac{1}{30}$ work in one day, the number of days B needs to complete the work = $\frac{\frac{122}{150}}{\frac{1}{30}} =24\frac{2}{5}$ days Hence, the correct answer is $24 \frac{2}{5}$.
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Question : Rekha alone can complete a task in 16 days and Bina alone can complete the same task in 12 days. Starting with Rekha, they work on alternate days. The task will be completed in:
Option 1: $12 \frac{3}{4}\ \text{days}$
Option 2: $12\ \text{days}$
Option 3: $13\ \text{days}$
Option 4: $13 \frac{3}{4}\ \text{days}$
Question : A can do a task in 8 days, while B can do it in 18 days. In how many days will the work be completed if they both work on alternate days, starting with B?
Option 1: $11 \frac{1}{3}$ days
Option 2: $12 \frac{1}{3}$ days
Option 3: $10$ days
Option 4: $10 \frac{1}{3}$ days
Question : 30 men can complete a work in 12 days. After 6 days, 24 more men joined them. How many days will it now take to complete the remaining work?
Option 1: $3\frac{1}{3}$ days
Option 2: $3\frac{2}{3}$ days
Option 3: $3\frac{1}{2}$ days
Option 4: $2\frac{1}{3}$ days
Question : Amar can complete a work in 15 days and Prem in 12 days. Starting with Amar, they work on alternate days. In how many days will the work be completed?
Option 1: $13\frac{2}{5}$
Option 2: $12\frac{1}{6}$
Option 3: $13\frac{1}{2}$
Option 4: $13$
Question : Virat can complete a task in 30 days and Daniel is 60% more efficient than Virat in completing the same task. Find the time total taken by Daniel to complete the task.
Option 1: $16 \frac{3}{5}$ days
Option 2: $18 \frac{3}{4}$ days
Option 3: $19 \frac{5}{3}$ days
Option 4: $17 \frac{5}{3}$ days
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