Practice Questions
Concept Explanation
When workers cooperate, daily rates add.
Key Formulas
- A in a days, B in b days ⇒ together: 1/a + 1/b per day
- Together time = ab/(a + b) days
- Three workers: add 1/a + 1/b + 1/c
Example
A in 12 days, B in 18 days. Together rate = 1/12 + 1/18 = 5/36. Time = 36/5 = 7.2 days.
Common Trap
Rates add only when they work simultaneously, not when they take turns unless stated.
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Q1 Easy
A can finish a work in 10 days and B can finish the same work in 15 days. If they work together, in how many days will they finish the work?
ExplanationTogether time = (10 × 15)/(10 + 15) = 6 days. -
Q2 Medium
A alone can complete a work in 12 days and B alone can complete it in 18 days. How many days will they take to finish the work if they work together?
ExplanationTogether time = (12 × 18)/(12 + 18) = 7.2 days. -
Q3 Medium
A can finish a work in 8 days and B can finish the same work in 24 days. What part of the work do they complete together in one day?
ExplanationCombined daily rate = 1/8 + 1/24 = 4/24 = 1/6. -
Q4 Easy
A can do a piece of work in 6 days and B can do the same work in 12 days. In how many days will they finish the work if they work together?
ExplanationTogether time = (6 × 12)/(6 + 12) = 4 days. -
Q5 Easy
A can complete a work in 20 days and B can complete it in 30 days. How many days will they take to finish the work together?
ExplanationTogether time = (20 × 30)/(20 + 30) = 12 days. -
Q6 Hard
A, B and C can finish a work alone in 12 days, 15 days and 20 days respectively. In how many days will they finish the work if all three work together?
ExplanationCombined rate = 1/12 + 1/15 + 1/20 = 1/5. Time = 5 days. -
Q7 Easy
A can finish a work in 9 days and B can finish it in 18 days. How many days will A and B take to finish the work together?
ExplanationTogether time = (9 × 18)/(9 + 18) = 6 days.
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Q8 Medium
A can complete a work in 4 days and B can complete it in 12 days. What fraction of the work is completed by them together in one day?
ExplanationCombined daily rate = 1/4 + 1/12 = 1/3. -
Q9 Hard
A can finish a work in 14 days and B can finish it in 21 days. How many days will they take to finish the work together?
ExplanationTogether time = (14 × 21)/(14 + 21) = 8.4 days. -
Q10 Easy
A can do a work in 5 days and B can do the same work in 20 days. In how many days will they finish the work if they work together?
ExplanationTogether time = (5 × 20)/(5 + 20) = 4 days. -
Q11 Hard
A and B together can finish a work in 6 days. A alone can finish the same work in 10 days. In how many days can B alone finish the work?
Explanation1/B = 1/6 − 1/10 = 1/15. So B alone takes 15 days. -
Q12 Medium
A can finish a work in 24 days and B can finish it in 8 days. How many days will they take to finish the work together?
ExplanationTogether time = (24 × 8)/(24 + 8) = 6 days. -
Q13 Medium
A can finish a work in 16 days and B can finish it in 24 days. What fraction of the work is completed if they work together for 4 days?
ExplanationCombined rate = 5/48. Work in 4 days = 4 × 5/48 = 5/12. -
Q14 Easy
A can complete a work in 3 days and B can complete it in 6 days. In how many days will they finish the work if they work together?
ExplanationTogether time = (3 × 6)/(3 + 6) = 2 days.
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DS1 Easy
In how many days can A and B finish the work together?
Statement IA alone can finish the work in 10 days.
Statement IIB alone can finish the work in 15 days.
ExplanationBoth individual times are needed: (10 × 15)/(10 + 15) = 6 days. -
DS2 Easy
What fraction of the work is completed by A and B together in one day?
Statement IA alone can finish the work in 8 days.
Statement IIB alone can finish the work in 24 days.
ExplanationTogether they complete 1/8 + 1/24 = 1/6 of the work in one day.
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DS3 Medium
In how many days can A and B finish the work together?
Statement IA and B together can finish the work in 4 days.
Statement IIA alone can finish the work in 6 days.
ExplanationStatement I alone directly gives the together time as 4 days. -
DS4 Medium
In how many days can B alone finish the work?
Statement IA and B together can finish the work in 6 days.
Statement IIA alone can finish the work in 10 days.
Explanation1/B = 1/6 − 1/10 = 1/15, so B alone takes 15 days.