The cost of `2(1)/(2)` meters of cloth is Rs`78(3)/(4)` . Find the cost of cloth per metre.

Answer

To find the cost of cloth per meter, we will follow these steps:

### Step 1: Convert the mixed numbers to improper fractions
1. The length of the cloth is given as \(2 \frac{1}{2}\) meters.
- To convert this to an improper fraction:
\[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]

2. The cost of the cloth is given as \(Rs. 78 \frac{3}{4}\).
- To convert this to an improper fraction:
\[ 78 \frac{3}{4} = \frac{78 \times 4 + 3}{4} = \frac{312 + 3}{4} = \frac{315}{4} \]

### Step 2: Set up the equation for cost per meter
Now, we know that the cost of \( \frac{5}{2} \) meters of cloth is \( \frac{315}{4} \) Rs. We need to find the cost of 1 meter of cloth.

### Step 3: Calculate the cost per meter
To find the cost per meter, we divide the total cost by the total meters:
\[ \text{Cost per meter} = \frac{\text{Total Cost}}{\text{Total Meters}} = \frac{\frac{315}{4}}{\frac{5}{2}} \]

### Step 4: Simplify the division of fractions
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{\frac{315}{4}}{\frac{5}{2}} = \frac{315}{4} \times \frac{2}{5} = \frac{315 \times 2}{4 \times 5} = \frac{630}{20} \]

### Step 5: Simplify the result
Now, we simplify \( \frac{630}{20} \):
\[ \frac{630 \div 10}{20 \div 10} = \frac{63}{2} \]

### Step 6: Convert to mixed number (if needed)
The cost per meter can also be expressed as a mixed number:
\[ \frac{63}{2} = 31 \frac{1}{2} \]

### Final Answer
The cost of cloth per meter is \( Rs. 31 \frac{1}{2} \) or \( Rs. 31.50 \).

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