Question : A is two times as efficient as B. A can complete a work in 20 days less than B. If both of them work together, then in how many days will the same work be completed?
Option 1: $\frac{40}{3}$ days
Option 2: $\frac{27}{2}$ days
Option 3: 20 days
Option 4: 15 days
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Correct Answer: $\frac{40}{3}$ days
Solution : Given: A is two times as efficient as B. A can complete a work in 20 days less than B. Use the formulas, $\text{Time}=\frac{\text{Total work}}{\text{Efficiency}}$ The relationship between time and efficiency is inversely proportional when the work is equal. The efficiencies of A : B = 2 : 1 ⇒ The time taken of A : B = 1 : 2 A's one day work = $\frac{1}{20}$ B's one day work = $\frac{1}{40}$ (A + B)'s one day work = $\frac{1}{20}+\frac{1}{40}=\frac{3}{40}$ days The time taken to complete the same work = $\frac{40}{3}$ days Hence, the correct answer is $\frac{40}{3}$ days.
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Question : P is thrice as good as a workman as Q and therefore can finish a work in 40 days less than Q. In how many days can they together complete the same work?
Option 1: 20 days
Option 2: 15 days
Option 3: 22.5 days
Option 4: 18 days
Question : A can do a piece of work alone in 40 days. A and B together can do the same work in 10 days. C is 50% less efficient than B. In how many days can A and C together complete the same work?
Option 2: 24 days
Option 3: 16 days
Option 4: 12 days
Question : A and B together complete a work in 20 days, B and C together complete the same work in 30 days, and C and A together complete the same work in 24 days. In how many days A, B, and C together can complete the same work?
Option 1: 8 days
Option 2: 16 days
Option 3: 12 days
Question : A alone can complete a work in 16 days and B alone can complete the same work in 96 days. In how many days both A and B together can complete the same work?
Option 1: $\frac{88}{13}$ days
Option 2: $\frac{96}{7}$ days
Option 3: $\frac{96}{13}$ days
Option 4: $\frac{88}{14}$ days
Question : A, B, and C together can complete a work in 5 days. A and B together can complete the same work in 6 days. C alone can finish the same work in how many days?
Option 1: 60 days
Option 2: 30 days
Option 3: 15 days
Option 4: 20 days
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