One day a labourer earned Rs. `58""1/2`. Out of this money, he spent Rs. `18""3/4` on food and Rs. `6""1/5` on other needs. How much is left with him?

Options

A. Rs. `43""15/20`
B. Rs. `25""17/23`
C. Rs. `33""11/20`
D. Rs. `45""9/20`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. **Total money earned by the laborer**: Rs. 58 1/2
- Convert to improper fraction:
\[ 58 \times 2 + 1 = 116 + 1 = 117 \quad \text{so,} \quad \frac{117}{2} \]

2. **Money spent on food**: Rs. 18 3/4
- Convert to improper fraction:
\[ 18 \times 4 + 3 = 72 + 3 = 75 \quad \text{so,} \quad \frac{75}{4} \]

3. **Money spent on other needs**: Rs. 6 1/5
- Convert to improper fraction:
\[ 6 \times 5 + 1 = 30 + 1 = 31 \quad \text{so,} \quad \frac{31}{5} \]

### Step 2: Find Total Money Spent
1. **Add the amounts spent on food and other needs**:
\[ \text{Total money spent} = \frac{75}{4} + \frac{31}{5} \]

2. **Find the LCM of the denominators (4 and 5)**:
- The LCM of 4 and 5 is 20.

3. **Convert the fractions to have a common denominator**:
- For \(\frac{75}{4}\):
\[ \frac{75 \times 5}{4 \times 5} = \frac{375}{20} \]
- For \(\frac{31}{5}\):
\[ \frac{31 \times 4}{5 \times 4} = \frac{124}{20} \]

4. **Add the fractions**:
\[ \frac{375}{20} + \frac{124}{20} = \frac{375 + 124}{20} = \frac{499}{20} \]

### Step 3: Calculate Money Left
1. **Subtract the total money spent from the total money earned**:
\[ \text{Money left} = \frac{117}{2} - \frac{499}{20} \]

2. **Find the LCM of the denominators (2 and 20)**:
- The LCM of 2 and 20 is 20.

3. **Convert \(\frac{117}{2}\) to have a common denominator**:
\[ \frac{117 \times 10}{2 \times 10} = \frac{1170}{20} \]

4. **Now subtract the fractions**:
\[ \frac{1170}{20} - \frac{499}{20} = \frac{1170 - 499}{20} = \frac{671}{20} \]

### Step 4: Convert to Mixed Number
1. **Convert \(\frac{671}{20}\) to a mixed number**:
- Divide 671 by 20:
- 20 goes into 671 thirty-three times (33).
- Remainder: \(671 - 660 = 11\).
- So, \(\frac{671}{20} = 33 \frac{11}{20}\).

### Final Answer
The amount left with the laborer is Rs. \(33 \frac{11}{20}\).

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