Practice Questions
Concept Explanation
Work = Rate × Time. Treat total work as 1 unit unless stated otherwise.
Key Formulas
- If a person finishes in n days, daily rate = 1/n of the work.
- Time = Work / Rate
- Work done = Rate × Days worked
Example
A completes the work in 10 days. Daily rate = 1/10. In 4 days, work done = 4/10 = 2/5.
Common Trap
Do not multiply days directly unless rates are known. Always convert to work per day first.
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Q1 Easy
A alone can complete a piece of work in 12 days. What fraction of the work does he complete in one day?
ExplanationIf the full work is finished in 12 days, one day's work = 1/12 of the total work. -
Q2 Easy
A worker completes 1/8 of the work every day at a constant rate. How many days will he take to finish the entire work?
ExplanationTotal time = 1 ÷ (1/8) = 8 days. -
Q3 Easy
A worker completes 1/20 of the work each day. How much work will he complete in 5 days?
ExplanationWork done = 5 × (1/20) = 5/20 = 1/4. -
Q4 Medium
A completes 3/10 of a work in 6 days, working at the same rate every day. How many days will A take to finish the entire work alone?
ExplanationDaily rate = (3/10) ÷ 6 = 1/20. Total time = 1 ÷ (1/20) = 20 days. -
Q5 Easy
A worker's efficiency doubles while the amount of work remains unchanged. What happens to the time required to finish the work?
ExplanationWhen efficiency doubles, the daily work rate doubles, so the required time is halved. -
Q6 Easy
B can finish a work in 15 days. What fraction of the work does B complete in 5 days?
ExplanationFraction completed = 5/15 = 1/3. -
Q7 Medium
A worker completes 2/5 of the work each day. How many days will he need to finish the entire work?
ExplanationTotal time = 1 ÷ (2/5) = 5/2 = 2.5 days.
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Q8 Easy
C can complete the work in 24 days. What fraction of the work will C finish in 8 days?
ExplanationFraction completed = 8/24 = 1/3. -
Q9 Easy
Assuming the total work is 1 unit and a worker's daily rate is 1/30, how many days will he take to finish the work?
ExplanationTime = Work ÷ Rate = 1 ÷ (1/30) = 30 days. -
Q10 Medium
A worker completes 50% of the work in 4 days, working at a constant rate. How many days will he take to finish the entire work?
ExplanationHalf the work in 4 days means the full work takes 8 days. -
Q11 Hard
For the same amount of work, a worker takes 10 days at first and 15 days later. By what fraction does his daily work rate decrease?
ExplanationRate falls from 1/10 to 1/15. Decrease = (1/10 − 1/15) ÷ (1/10) = 1/3. -
Q12 Medium
A worker completes 1/6 of the work each day. After working for 1 day, how many more days does he need to finish the remaining work?
ExplanationTotal time = 6 days. After 1 day, 5 days of work remain. -
Q13 Easy
Which of the following is the correct relationship among work, rate, and time?
ExplanationThe fundamental relation is Work = Rate × Time. -
Q14 Easy
F can complete a work in 9 days. What fraction of the work is completed by F in 6 days?
ExplanationFraction completed = 6/9 = 2/3.
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DS1 Easy
How many days will it take to complete the work?
Statement IThe worker completes 1/10 of the work each day.
Statement IIThe worker completes 1/5 of the work in 2 days.
ExplanationEach statement gives the daily rate as 1/10, so the total time is 10 days. -
DS2 Easy
What fraction of the work is completed in 3 days?
Statement IThe entire work can be finished in 12 days.
Statement IIThe worker completes 1/12 of the work each day.
ExplanationEither statement gives the fraction completed in 3 days as 3/12 = 1/4.
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DS3 Medium
Is more than half of the work completed in 5 days?
Statement IThe entire work can be finished in 8 days.
Statement IIThe worker completes 1/6 of the work each day.
ExplanationStatement I: 5/8 > 1/2. Statement II: 5/6 > 1/2. Each statement alone is sufficient. -
DS4 Easy
What is the worker's daily work rate?
Statement IThe worker completes 1/4 of the work in 3 days.
Statement IIThe worker can finish the entire work in 12 days.
ExplanationBoth statements give the daily rate as (1/4)/3 = 1/12.