Question : A is twice as a good worker as B and together they finish the work in 20 days. In how many days can A alone do it?
Option 1: 25 days
Option 2: 36 days
Option 3: 20 days
Option 4: 30 days
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Correct Answer: 30 days
Solution :
Let the efficiency of B be $x$.
⇒ The efficiency of A is 2$x$.
Total number of days needed to complete the work if A and B worked together = 20 days
Total work done = Total number of days × Total efficiency
= 20 × ($x$ + 2$x$)
= 20 × 3$x$
= 60$x$
Number of days needed to complete the work if A worked alone
= $\frac{\text{Total work}}{\text{Efficiency of A}}$
= $\frac{60x}{2x}$
= 30 days
Hence, the correct answer is 30 days.
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