What is the average daily wages of a worker who works five days if he made Rs. 80 the first day ?
I. The corker made a total of Rs. 400 for the first four days of work.
II. The worker made `20%` more each day than he did on the previous day.

Answer

To solve the problem of finding the average daily wages of a worker who works five days, given that he made Rs. 80 on the first day, we need to analyze the two statements provided.

### Step 1: Analyze Statement I
Statement I states that the worker made a total of Rs. 400 for the first four days of work.

1. **Calculate the total earnings for the first four days:**
- Let the earnings for the first day be Rs. 80.
- Let the earnings for the second, third, and fourth days be \( x_2, x_3, x_4 \) respectively.
- According to Statement I, we have:
\[ x_1 + x_2 + x_3 + x_4 = 400 \]
- Substituting \( x_1 = 80 \):
\[ 80 + x_2 + x_3 + x_4 = 400 \]
- This simplifies to:
\[ x_2 + x_3 + x_4 = 320 \]
- We still do not know how much the worker earned on the fifth day, \( x_5 \). Therefore, we cannot determine the average daily wage from this statement alone.

**Conclusion for Statement I:** Not sufficient.

### Step 2: Analyze Statement II
Statement II states that the worker made 20% more each day than he did on the previous day.

1. **Calculate the earnings for each day:**
- Day 1: \( x_1 = 80 \)
- Day 2:
\[ x_2 = x_1 + 0.2 \times x_1 = 80 + 0.2 \times 80 = 80 + 16 = 96 \]
- Day 3:
\[ x_3 = x_2 + 0.2 \times x_2 = 96 + 0.2 \times 96 = 96 + 19.2 = 115.2 \]
- Day 4:
\[ x_4 = x_3 + 0.2 \times x_3 = 115.2 + 0.2 \times 115.2 = 115.2 + 23.04 = 138.24 \]
- Day 5:
\[ x_5 = x_4 + 0.2 \times x_4 = 138.24 + 0.2 \times 138.24 = 138.24 + 27.648 = 165.888 \approx 165.89 \]

2. **Calculate the total earnings over the five days:**
\[ \text{Total earnings} = x_1 + x_2 + x_3 + x_4 + x_5 = 80 + 96 + 115.2 + 138.24 + 165.89 \]
- Adding these amounts:
\[ 80 + 96 + 115.2 + 138.24 + 165.89 = 595.33 \]

3. **Calculate the average daily wage:**
\[ \text{Average daily wage} = \frac{\text{Total earnings}}{5} = \frac{595.33}{5} = 119.066 \approx 119.06 \]

**Conclusion for Statement II:** Sufficient.

### Final Conclusion
- Statement I alone is not sufficient to determine the average daily wages.
- Statement II alone is sufficient to determine the average daily wages.