Practice Questions
Concept Explanation
Find total or remaining time when work starts, stops, or workers join or leave mid-way.
Key Formulas
- Remaining work = 1 − Work completed
- Remaining time = Remaining work / Current rate
- If a worker leaves, recalculate combined rate with remaining workers
Example
A alone 10 days. After 3 days, 3/10 done, 7/10 left ⇒ 7 more days for A alone.
Common Trap
After partial work, use remaining work, not total work, with the new rate.
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Q1 EasyA alone can finish a work in 10 days. After working alone for 3 days, how many more days will A need to finish the remaining work?ExplanationWork done = 3/10. Remaining work = 7/10. Time left = 7 days.
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Q2 EasyA can finish a work in 20 days. After working alone for 5 days, he finds that 1/4 of the work is completed. How many more days will A need to finish the remaining work?ExplanationSince 1/4 is done in 5 days, the full work takes 20 days. Remaining time = 15 days.
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Q3 EasyA and B together can finish a work in 12 days. After working together for 4 days, 1/3 of the work is completed. How many more days will they take to finish the remaining work if they continue together?ExplanationIf 1/3 is done in 4 days, the full work takes 12 days. Remaining time = 8 days.
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Q4 EasyA can finish a work in 12 days. After working alone for 4 days, what fraction of the work is still remaining?ExplanationWork done = 1/3. Remaining work = 2/3.
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Q5 EasyA can finish a work in 9 days. After working alone for 3 days, how many more days will A need to finish the remaining work?ExplanationWork done = 1/3. Remaining work = 2/3. Time left = 6 days.
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Q6 MediumA can finish a work in 12 days and B can finish it in 24 days. They work together for 4 days and then A alone finishes the remaining work. In how many days will A finish the rest?ExplanationTogether they complete 1/2 of the work in 4 days. A alone finishes the remaining half in 6 days.
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Q7 MediumA can finish a work in 10 days and B can finish it in 15 days. They work together for 3 days and then B alone finishes the remaining work. In how many days will B finish the rest?ExplanationHalf the work is done in 3 days. B alone finishes the remaining half in 7.5 days.
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Q8 MediumA can finish a work in 6 days and B can finish it in 12 days. They work together for 2 days and then A alone finishes the remaining work. In how many days will A finish the rest?ExplanationHalf the work is done in 2 days. A alone finishes the remaining half in 3 days.
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Q9 MediumA can finish a work in 10 days and B can finish it in 20 days. They work together for 4 days. What fraction of the work is still remaining?ExplanationTogether they complete 3/20 per day. In 4 days, work done = 3/5. Remaining work = 2/5.
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Q10 MediumA can finish a work in 8 days and B can finish it in 16 days. They work together for 4 days and then B alone finishes the remaining work. In how many days will B finish the rest?ExplanationTogether they complete 3/4 of the work in 4 days. B alone finishes the remaining 1/4 in 4 days.
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Q11 HardA and B together can finish a work in 6 days. A alone can finish it in 10 days. They work together for 2 days and then B alone finishes the remaining work. In how many days will B finish the rest?ExplanationWork done in 2 days = 1/3. Remaining work = 2/3. B alone takes (2/3)/(1/15) = 10 days.
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Q12 HardA can finish a work in 15 days and B can finish it in 30 days. They work together for 5 days and then B alone finishes the remaining work. In how many days will B finish the rest?ExplanationTogether they complete 1/2 of the work in 5 days. B alone finishes the remaining half in 15 days.
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Q13 HardA alone can finish a work in 8 days. After working alone for 2 days, C joins him and they finish the remaining work in 3 more days. In how many days can C alone finish the work?ExplanationRemaining 3/4 of the work is finished in 3 days by A and C together. So A + C rate = 1/4. C alone takes 8 days.
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Q14 HardA can finish a work in 18 days. After working alone for 6 days, B joins him and they finish the remaining work in 6 more days. In how many days can B alone finish the work?ExplanationRemaining 2/3 of the work is finished in 6 days by A and B together. So B alone takes 18 days.
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DS1 Easy
How many more days does A need to finish the work?
Statement IA alone can finish the work in 10 days.
Statement IIA has already worked for 3 days.
ExplanationRemaining work = 7/10. A needs 7 more days. -
DS2 Easy
Is the work completed after 4 days?
Statement IA alone can finish the work in 12 days.
Statement IIOnly A works for 4 days.
ExplanationAfter 4 days only 1/3 of the work is done, so the work is not completed.
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DS3 Medium
In how many days can B alone finish the remaining work?
Statement IA alone can finish the work in 10 days and B alone in 15 days.
Statement IIA and B work together for 2 days.
ExplanationWork done in 2 days = 1/3. B alone finishes the remaining 2/3 in 10 days. -
DS4 Medium
In how many days can A alone finish the remaining work?
Statement IA alone can finish the work in 12 days and B alone in 24 days.
Statement IIA and B work together for 4 days.
ExplanationHalf the work is done in 4 days. A alone finishes the remaining half in 6 days.