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
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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