Practice Questions
Concept Explanation
Individual work problems find how long one person takes alone, or how much is done in a given period.
Key Formulas
- Days alone = Total work / Person's daily rate
- Remaining days = Total days − Days already worked
- Remaining work = 1 − Work already done
Example
A alone finishes in 12 days. After 5 days, work left = 1 − 5/12 = 7/12; days left = 7 days.
Common Trap
Calendar days with holidays differ from working days. Read whether absence extends total time.
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Q1 Easy
A alone can finish a piece of work in 10 days. How many days will A take to complete the work if he works alone throughout?
ExplanationThe question itself gives that A alone finishes the work in 10 days. -
Q2 Easy
A can complete a work in 18 days. He works alone for 6 days and then stops. How many more days will A need to finish the remaining work alone?
ExplanationRemaining time = 18 − 6 = 12 days. -
Q3 Easy
A can finish a work in 20 days. After working alone for 4 days, what fraction of the work is still remaining?
ExplanationWork done = 4/20 = 1/5. Remaining work = 1 − 1/5 = 4/5. -
Q4 Medium
A can complete the work in 15 days by working 8 hours a day. If he works 10 hours a day at the same efficiency, in how many days will he finish the work?
ExplanationTotal work = 15 × 8 = 120 man-hours. Required days = 120/10 = 12 days. -
Q5 Medium
A completes 75% of a work in 9 days, working at a constant rate. How many days will A take to finish the entire work alone?
ExplanationIf 75% takes 9 days, the full work takes 9 ÷ 0.75 = 12 days. -
Q6 Easy
A can complete the work in 24 days. What fraction of the work will A complete in 6 days?
ExplanationFraction completed = 6/24 = 1/4. -
Q7 Medium
A takes 16 days to complete a piece of work. If the work becomes twice as large but A works at the same rate, how many days will A need?
ExplanationWhen the work doubles and the rate stays the same, the required time also doubles to 32 days.
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Q8 Hard
A alone can finish a work in 30 days and B alone can finish the same work in 20 days. By what percent is A less efficient than B?
ExplanationEfficiency ratio A:B = 20:30 = 2:3. A is (3 − 2)/3 = 33.33% less efficient than B. -
Q9 Easy
A can complete a work in 40 days. How many days will A take to complete half of the work?
ExplanationAt a constant rate, half the work takes half the time = 20 days. -
Q10 Easy
A completes 1/7 of the work each day. How many days will he take to finish the entire work?
ExplanationTotal time = 1 ÷ (1/7) = 7 days. -
Q11 Hard
A can finish a work in 14 working days, but he remains idle for 2 days in between. If no one else helps him, how many calendar days will he take to finish the work?
ExplanationHe still needs 14 working days, but those are spread over 16 calendar days because of 2 idle days. -
Q12 Medium
A completes 2/5 of a work in 8 days. How many days will A take to finish the entire work alone?
ExplanationDaily rate = (2/5)/8 = 1/20. Total time = 20 days. -
Q13 Easy
A can finish a work in 9 days. If the amount of work doubles but A works at the same rate, how many days will he need now?
ExplanationWhen the work doubles, the required time doubles from 9 days to 18 days. -
Q14 Easy
A can complete the work in 12 days. After working alone for 8 days, what fraction of the work is still left?
ExplanationWork done = 8/12 = 2/3. Remaining work = 1/3.
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DS1 Easy
How many days does A take to finish the work alone?
Statement IA completes 1/4 of the work in 3 days.
Statement IIA completes 1/2 of the work in 6 days.
ExplanationEach statement gives A's daily rate as 1/12, so A alone takes 12 days. -
DS2 Easy
How many more days does A need to finish the work?
Statement IA alone can finish the work in 20 days.
Statement IIA has already worked for 8 days.
ExplanationBoth total time and elapsed time are needed: 20 − 8 = 12 days remain.
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DS3 Easy
What fraction of the work is still remaining?
Statement IA can finish the work in 15 days.
Statement IIA has already worked for 5 days.
ExplanationWork done = 5/15 = 1/3. Remaining work = 2/3. -
DS4 Medium
Can A finish the work within 10 days?
Statement IA alone takes 12 days to finish the work.
Statement IIA works 8 hours per day.
ExplanationStatement I alone shows that A needs 12 days, so he cannot finish within 10 days. Statement II does not fix the total work hours.