Practice Questions
Concept Explanation
Efficiency is work done per unit time. Higher efficiency means shorter time for the same work.
Key Formulas
- Efficiency ratio = inverse of time ratio (same work)
- If A is k times as efficient as B, A's time = B's time / k
- Work = Efficiency × Time
Example
A is twice as efficient as B. B takes 16 days ⇒ A takes 8 days.
Common Trap
Efficiency and time are inversely proportional for the same work.
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Q1 Easy
A is twice as efficient as B. If B can finish a work in 16 days, in how many days can A finish the same work?
ExplanationFor the same work, A takes half the time taken by B. So A takes 8 days. -
Q2 Medium
A is 50% more efficient than B. If B can finish a work in 18 days, in how many days can A finish the same work?
ExplanationA's efficiency is 1.5 times B's efficiency, so A's time = 18/1.5 = 12 days. -
Q3 Medium
The efficiencies of A and B are in the ratio 3:2. If A can finish a work in 12 days, in how many days can B finish the same work?
ExplanationTime is inversely proportional to efficiency. Time ratio A:B = 2:3, so B takes 18 days. -
Q4 Easy
A can finish a work in 10 days and B can finish the same work in 15 days. What is the ratio of their efficiencies?
ExplanationEfficiency is inversely proportional to time: 1/10 : 1/15 = 3:2. -
Q5 Easy
A is three times as efficient as B. If A can finish a work in 6 days, in how many days can B finish the same work?
ExplanationB takes three times as long as A. So B takes 18 days. -
Q6 Hard
The efficiencies of A, B and C are in the ratio 2:3:4. If C can finish a work in 10 days, in how many days can A finish the same work?
ExplanationTime ratio A:C = 4:2 = 2:1. So A takes twice as long as C, which is 20 days. -
Q7 Medium
A is 20% less efficient than B. If B can finish a work in 12 days, in how many days can A finish the same work?
ExplanationA's efficiency is 80% of B's efficiency. So A's time = 12/0.8 = 15 days.
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Q8 Medium
A can finish a work in 8 days and B can finish the same work in 12 days. How many times as efficient is A as B?
ExplanationEfficiency ratio = 12:8 = 1.5. -
Q9 Hard
A is twice as efficient as B and three times as efficient as C. If B can finish a work in 24 days, in how many days can C finish the same work?
ExplanationB takes 24 days, so A takes 12 days. Since A is thrice as efficient as C, C takes 36 days. -
Q10 Medium
The efficiencies of A and B are in the ratio 5:4. If B can finish a work in 20 days, in how many days can A finish the same work?
ExplanationTime ratio A:B = 4:5. So A takes 20 × 4/5 = 16 days. -
Q11 Easy
If a worker's efficiency doubles while the amount of work remains the same, what happens to the time required to finish the work?
ExplanationEfficiency and time are inversely proportional for the same work. -
Q12 Hard
A is 25% more efficient than B. If A can finish a work in 10 days, in how many days can B finish the same work?
ExplanationB takes 25% more time than A. So B's time = 10 × 1.25 = 12.5 days. -
Q13 Medium
A can finish a work in 6 days and B can finish the same work in 9 days. By what percent is A more efficient than B?
ExplanationEfficiency ratio = 9:6 = 1.5. So A is 50% more efficient than B. -
Q14 Hard
A, B and C take 2, 3 and 4 days respectively to finish the same work. What is the ratio of their efficiencies?
ExplanationEfficiency is inversely proportional to time: 1/2 : 1/3 : 1/4 = 6:4:3.
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DS1 Easy
In how many days can A finish the work?
Statement IA is twice as efficient as B.
Statement IIB can finish the work in 16 days.
ExplanationA takes half the time taken by B, so A takes 8 days. -
DS2 Medium
In how many days can B finish the work?
Statement IA is 50% more efficient than B.
Statement IIA can finish the work in 12 days.
ExplanationB takes 18 days.
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DS3 Easy
What is the ratio of the efficiencies of A and B?
Statement IA alone can finish the work in 10 days.
Statement IIB alone can finish the work in 15 days.
ExplanationEfficiency ratio = 1/10 : 1/15 = 3:2. -
DS4 Medium
Is A more than twice as efficient as B?
Statement IA can finish the work in 6 days and B can finish it in 15 days.
Statement IIA can finish the work in 6 days.
ExplanationEfficiency ratio = 15:6 = 2.5, which is more than 2.