We are given that Arun is 25% more efficient than Dev, and Dev completes the work in 20 days. To find how long it will take Arun to complete the same work, we use the relationship between efficiency and time.

Step 1: Efficiency and Time Relationship

Efficiency and time are inversely proportional. If someone is more efficient, they will take less time to complete the same work.

Let Dev's efficiency be $E_D$ and Arun's efficiency be $E_A$. Since Arun is 25% more efficient than Dev: $E_A = E_D + 0.25E_D = 1.25E_D$

Step 2: Time Taken by Arun

The time taken by a worker is inversely proportional to their efficiency, so the time taken by Arun (denoted by $T_A$) is related to Dev's time $T_D$ as: $T_A = \frac{T_D \times E_D}{E_A} = \frac{T_D}{1.25}$

Step 3: Substituting the Values

Dev takes 20 days to complete the work, so $T_D = 20$: $T_A = \frac{20}{1.25} = 16 \text{ days}$

Thus, Arun will take 16 days to complete the work.

Answer:

The correct option is 16 days.

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Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. If Arun were 50% more efficient than Dev, how many days would he take to complete the work?
2. If Dev could complete the work in 30 days, how many days would Arun take, given the same 25% increased efficiency?
3. If a third person, Riya, is 10% less efficient than Dev, how many days would Riya take to complete the work?
4. How long would it take Dev and Arun together to complete the work?
5. If Arun worked alone for the first 8 days and then Dev joined him, how many more days would it take them together to finish the work?

Tip:

When dealing with efficiency problems, remember that time is inversely proportional to efficiency: $\text{Time} \propto \frac{1}{\text{Efficiency}}$.