Practice Questions
Concept Explanation
Mixed problems combine individual work, combined rates, wages, and partial completion in one question.
Strategy
- Convert every worker or pipe to a daily rate first.
- Split the timeline into stages when workers join or leave.
- For wages, share payment in the ratio of work done.
- Check whether workers work simultaneously or on alternate days.
Example
A in 10 days, B in 15 days. Together 3 days, then A alone: done = 3/6 = 1/2; A finishes rest in 5 days. Total = 8 days.
Common Trap
Do not mix calendar days with working days without converting.
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Q1 Medium
A can finish a work in 10 days and B can finish it in 15 days. They work together for 3 days and then A alone finishes the remaining work. In how many total days is the work completed?
ExplanationHalf the work is done in 3 days. A alone finishes the rest in 5 days. Total = 8 days. -
Q2 Hard
A can finish a work in 12 days and B can finish it in 18 days. They work together for 6 days and then B alone finishes the remaining work. In how many total days is the work completed?
ExplanationHalf the work is done in 6 days. B alone finishes the rest in 6 days. Total = 12 days. -
Q3 Medium
A can finish a work in 8 days and B can finish it in 24 days. They work together and receive Rs. 1,200 for the work. How much should A receive?
ExplanationWage ratio A:B = 3:1. A receives 3/4 × 1200 = Rs. 900. -
Q4 Easy
A can finish a work in 6 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. Four cycles complete the work in 8 days. -
Q5 Easy
If 5 men can finish a work in 12 days, in how many days can 8 men finish the same work?
ExplanationTotal work = 60 man-days. Time for 8 men = 7.5 days. -
Q6 Medium
A tap can fill a tank in 10 hours and a leak can empty the full tank in 15 hours. What is the effective time taken to fill the tank when both are working?
ExplanationEffective filling rate = 1/30. Time to fill = 30 hours. -
Q7 Easy
A is twice as efficient as B. If B can finish a work in 14 days, in how many days can A finish the same work?
ExplanationA takes half the time taken by B, so A takes 7 days.
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Q8 Easy
A can finish a work in 10 days and B can finish it in 15 days. In how many days can they finish the work together?
ExplanationTogether time = (10 × 15)/(10 + 15) = 6 days. -
Q9 Medium
If 2 men can do as much work as 3 women, and 6 men can finish a work in 10 days, in how many days can 9 women finish the same work?
ExplanationTotal work = 60 man-days = 90 woman-days. Time for 9 women = 10 days. -
Q10 Easy
A 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. -
Q11 Medium
An inlet pipe can fill a tank in 12 hours and an outlet pipe can empty the full tank in 18 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationNet filling rate = 1/36. Time to fill = 36 hours. -
Q12 Hard
A and B together can finish a work in 8 days. A alone can finish the same work in 12 days. In how many days can B alone finish the work?
Explanation1/B = 1/8 − 1/12 = 1/24. So B alone takes 24 days. -
Q13 Medium
A can finish a work in 9 days and B can finish it in 18 days. They work together for 3 days. What fraction of the work is still remaining?
ExplanationTogether they complete 1/6 per day. In 3 days, half the work is done and half remains. -
Q14 Hard
A can finish a work in 16 days and B can finish it in 24 days. They work together for 8 days and then A alone finishes the remaining work. In how many more days will A finish the rest?
ExplanationTogether they complete 5/6 of the work in 8 days. A alone finishes the remaining 1/6 in 8/3 days.
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DS1 Medium
What is the total time taken to finish the work?
Statement IA alone can finish the work in 10 days and B alone in 15 days.
Statement IIThey work together for 3 days and then A alone finishes the remaining work.
ExplanationHalf the work is done in 3 days. A alone needs 5 more days. Total = 8 days. -
DS2 Medium
How much should A receive from the total payment of Rs. 1,200?
Statement IA alone can finish the work in 8 days and B alone in 24 days.
Statement IIThey finish the work together.
ExplanationWage ratio A:B = 3:1. A receives Rs. 900.
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DS3 Easy
In how many days can 8 men finish the work?
Statement I5 men can finish the work in 12 days.
Statement IIThe amount of work remains unchanged.
ExplanationStatement I alone gives total work = 60 man-days, so 8 men need 7.5 days. -
DS4 Medium
What is the effective time taken to fill the tank?
Statement IA tap can fill the tank in 10 hours.
Statement IIA leak can empty the full tank in 15 hours.
ExplanationEffective filling rate is 1/30, so the tank is filled in 30 hours.