Find the cost of `3(2)/(5) ` metres of cloth at Rs. `63(3)/(4)` per metre.

Answer

To find the cost of \(3 \frac{2}{5}\) metres of cloth at Rs. \(63 \frac{3}{4}\) per metre, we will follow these steps:

### Step 1: Convert the mixed fractions to improper fractions

1. **Cost per metre**:
- The cost is given as \(63 \frac{3}{4}\).
- To convert it to an improper fraction, we multiply the whole number (63) by the denominator (4) and add the numerator (3):
\[ 63 \times 4 + 3 = 252 + 3 = 255 \]
- Thus, the cost per metre in improper fraction form is:
\[ \frac{255}{4} \]

2. **Length of cloth**:
- The length is given as \(3 \frac{2}{5}\).
- To convert it to an improper fraction, we multiply the whole number (3) by the denominator (5) and add the numerator (2):
\[ 3 \times 5 + 2 = 15 + 2 = 17 \]
- Thus, the length of cloth in improper fraction form is:
\[ \frac{17}{5} \]

### Step 2: Calculate the total cost

The total cost can be calculated using the formula:
\[ \text{Total Cost} = \text{Cost per metre} \times \text{Length of cloth} \]
Substituting the values we found:
\[ \text{Total Cost} = \frac{255}{4} \times \frac{17}{5} \]

### Step 3: Multiply the fractions

To multiply the fractions:
\[ \text{Total Cost} = \frac{255 \times 17}{4 \times 5} \]

Calculating the numerator:
\[ 255 \times 17 = 4335 \]

Calculating the denominator:
\[ 4 \times 5 = 20 \]

So, we have:
\[ \text{Total Cost} = \frac{4335}{20} \]

### Step 4: Simplify the fraction

To simplify \(\frac{4335}{20}\):
- We can divide both the numerator and the denominator by 5:
\[ \frac{4335 \div 5}{20 \div 5} = \frac{867}{4} \]

### Final Step: Convert to mixed fraction

To convert \(\frac{867}{4}\) to a mixed fraction:
- Divide 867 by 4:
\[ 867 \div 4 = 216 \quad \text{(remainder 3)} \]
Thus, we can express it as:
\[ 216 \frac{3}{4} \]

### Conclusion

The total cost of \(3 \frac{2}{5}\) metres of cloth at Rs. \(63 \frac{3}{4}\) per metre is:
\[ \text{Cost} = 216 \frac{3}{4} \text{ rupees} \]