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 Medium
A 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. -
Q2 Medium
A 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. -
Q3 Easy
A 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. -
Q4 Easy
A 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. -
Q5 Medium
A 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. -
Q6 Hard
A 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. -
Q7 Easy
A 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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Q8 Hard
A 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. -
Q9 Medium
A 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. -
Q10 Medium
A 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. -
Q11 Easy
A 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. -
Q12 Medium
A 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. -
Q13 Hard
A 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. -
Q14 Medium
A 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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DS1 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. -
DS2 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.
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DS3 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. -
DS4 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.