To solve this problem, we can follow these steps:

Step 1: Determine Amit's work rate

Amit can complete the work in 20 days, so his rate of work per day is: $\text{Amit's rate} = \frac{1}{20} \text{ work per day}.$

Step 2: Determine Ranjit's efficiency

Ranjit is 25% more efficient than Amit, which means Ranjit works at 125% of Amit's rate. In decimal form, this is: $\text{Ranjit's rate} = 1.25 \times \text{Amit's rate} = 1.25 \times \frac{1}{20}.$

Step 3: Calculate Ranjit's work rate

$\text{Ranjit's rate} = \frac{1.25}{20} = \frac{5}{80} = \frac{1}{16} \text{ work per day}.$

Step 4: Determine the number of days Ranjit takes

Since Ranjit's rate is $\frac{1}{16}$ work per day, the number of days he takes to complete the work is the reciprocal of his rate: $\text{Number of days} = \frac{1}{\text{Ranjit's rate}} = \frac{1}{\frac{1}{16}} = 16 \text{ days}.$

Thus, Ranjit will take 16 days to complete the same work.

Would you like further clarification or additional details?

Here are 5 related questions:

1. How long would it take both Amit and Ranjit to complete the work together?
2. If Amit works for 10 days and then Ranjit finishes the rest, how long would Ranjit take?
3. What is the efficiency increase required for Ranjit to finish the work in 12 days?
4. How many days would Amit take if his efficiency was reduced by 20%?
5. If Ranjit worked at 150% of Amit's efficiency, how many days would he take?

Tip: Efficiency problems often revolve around the idea that more efficiency translates to less time to complete the same task. Keep this proportional relationship in mind for similar problems!