Practice Questions
Concept Explanation
When workers alternate days, add the work done in one full cycle (each worker's turn).
Key Formulas
- Cycle work = sum of individual day rates in one round
- Total days ≈ (number of full cycles × cycle length) + extra days
- Starting worker affects which days count
Example
A alone 10 days, B alone 15 days, alternate from A. Two-day cycle = 1/10 + 1/15 = 1/6. The work is finished in 12 days.
Common Trap
Count partial cycles at the end; the last worker may not need a full day.
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Q1 EasyA can finish a work in 12 days and B can finish it in 6 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationWork done in every 2 days = 1/12 + 1/6 = 1/4. Four cycles complete the work in 8 days.
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Q2 EasyA and B can each finish a work alone in 10 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationEach completes 1/10 of the work on his working day. Five two-day cycles finish the work in 10 days.
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Q3 EasyA can finish a work in 4 days and B can finish it in 12 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationWork done in every 2 days = 1/4 + 1/12 = 1/3. Three cycles complete the work in 6 days.
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Q4 EasyA and B can each finish a work alone in 16 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationEach completes 1/16 of the work on his working day. Eight two-day cycles finish the work in 16 days.
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Q5 MediumA can finish a work in 10 days and B can finish it in 15 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationWork done in every 2 days = 1/10 + 1/15 = 1/6. Six such cycles complete the work in 12 days.
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Q6 MediumA can finish a work in 8 days and B can finish it in 24 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationWork done in every 2 days = 1/8 + 1/24 = 1/6. Six cycles complete the work in 12 days.
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Q7 MediumA can finish a work in 6 days and B can finish it in 12 days. They work on alternate days starting with A. What fraction of the work is completed in one full two-day cycle?ExplanationIn one cycle, A works on day 1 and B on day 2. Work done = 1/6 + 1/12 = 1/4.
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Q8 MediumA can finish a work in 9 days and B can finish it in 18 days. They work on alternate days starting with A. In how many days will half of the work be completed?ExplanationWork done in every 2 days = 1/6. Three cycles, or 6 days, complete half the work.
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Q9 MediumA can finish a work in 5 days and B can finish it in 20 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationWork done in every 2 days = 1/5 + 1/20 = 1/4. Four cycles complete the work in 8 days.
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Q10 MediumA can finish a work in 12 days and B can finish it in 18 days. They work on alternate days starting with A. What fraction of the work is completed in the first 6 days?ExplanationThree two-day cycles are completed in 6 days. Work done = 3 × (1/12 + 1/18) = 1/2.
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Q11 MediumA can finish a work in 7 days and B can finish it in 14 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationAfter 8 days, 4 cycles give 4 × 3/14 = 6/7 work. A completes the remaining work on the 9th day.
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Q12 HardA can finish a work in 20 days and B can finish it in 30 days. They work on alternate days starting with B. In how many days will the work be completed?ExplanationWork done in every 2 days = 1/20 + 1/30 = 1/12. Twelve cycles complete the work in 24 days.
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Q13 HardA can finish a work in 14 days and B can finish it in 21 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationAfter 16 days, 20/21 of the work is done. A completes the remaining work on the 17th day.
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Q14 HardA can finish a work in 10 days and B can finish it in 40 days. They work on alternate days starting with A. In how many days will the work be completed?ExplanationWork done in every 2 days = 1/10 + 1/40 = 1/8. Eight cycles complete the work in 16 days.
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DS1 Easy
Is the work completed within 10 days?
Statement IA alone can finish the work in 10 days and B alone in 10 days.
Statement IIA and B work on alternate days.
ExplanationSince both have the same rate, the work is completed exactly on the 10th day. -
DS2 Medium
In how many days will the work be completed?
Statement IA alone can finish the work in 10 days and B alone in 15 days.
Statement IIA and B work on alternate days starting with A.
ExplanationWork done in every 2 days = 1/6. Six cycles complete the work in 12 days.
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DS3 Medium
In how many days will the work be completed?
Statement IA alone can finish the work in 8 days and B alone in 24 days.
Statement IIA and B work on alternate days starting with A.
ExplanationWork done in every 2 days = 1/6. Total time = 12 days. -
DS4 Medium
What fraction of the work is completed in 6 days?
Statement IA alone can finish the work in 12 days and B alone in 18 days.
Statement IIA and B work on alternate days starting with A.
ExplanationThree two-day cycles are completed in 6 days. Work done = 1/2.