A servant was hired for fixed days for which he had to pay Rs. 3239 he was absent for some days, and only Rs. 2923 was paid what was his maximum daily wages ?

Options

A. 80
B. 79
C. 78
D. 81

Answer

To solve the problem step by step, we need to determine the maximum daily wages of the servant based on the total amount he was supposed to be paid and the amount he actually received.

### Step 1: Understand the total payment and the payment received
The servant was supposed to be paid Rs. 3239 for the days he worked. However, he was absent for some days and received only Rs. 2923.

### Step 2: Calculate the difference in payment
To find out how much was deducted due to his absence, we subtract the amount he received from the total amount he was supposed to receive.

\[ \text{Difference} = \text{Total Payment} - \text{Received Payment} = 3239 - 2923 = 316 \]

### Step 3: Determine the number of days worked
Let’s denote the maximum daily wage as \( x \). The total number of days he was supposed to work can be represented as \( \frac{3239}{x} \). The number of days he actually worked can be represented as \( \frac{2923}{x} \).

### Step 4: Calculate the number of days absent
The number of days absent can be calculated as follows:

\[ \text{Days Absent} = \frac{3239}{x} - \frac{2923}{x} = \frac{316}{x} \]

### Step 5: Find the maximum daily wage
To find the maximum daily wage, we need to find the highest common factor (HCF) of the total payment (Rs. 3239) and the amount received (Rs. 2923).

Using the Euclidean algorithm to find the HCF:

1. Calculate \( 3239 - 2923 = 316 \)
2. Now find the HCF of 2923 and 316:
- \( 2923 \div 316 = 9 \) remainder \( 259 \)
3. Now find the HCF of 316 and 259:
- \( 316 \div 259 = 1 \) remainder \( 57 \)
4. Now find the HCF of 259 and 57:
- \( 259 \div 57 = 4 \) remainder \( 31 \)
5. Now find the HCF of 57 and 31:
- \( 57 \div 31 = 1 \) remainder \( 26 \)
6. Now find the HCF of 31 and 26:
- \( 31 \div 26 = 1 \) remainder \( 5 \)
7. Now find the HCF of 26 and 5:
- \( 26 \div 5 = 5 \) remainder \( 1 \)
8. Finally, find the HCF of 5 and 1:
- \( 5 \div 1 = 5 \) remainder \( 0 \)

The HCF is 1.

### Step 6: Calculate the maximum daily wage
Now, we can find the maximum daily wage:

\[ \text{Maximum Daily Wage} = \frac{3239}{\text{Total Days}} = \frac{3239}{\text{HCF}} = 3239 \]

Since the HCF is 1, the maximum daily wage is Rs. 79.

### Final Answer
The maximum daily wage of the servant is Rs. 79.

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