Find the cost of `3(1)/(3)` metres of cloth at Rs `40(1)/(2)` per metre .

Answer

To find the cost of \(3 \frac{1}{3}\) metres of cloth at Rs \(40 \frac{1}{2}\) per metre, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. **Convert \(3 \frac{1}{3}\)**:
- The whole number part is 3 and the fractional part is \(\frac{1}{3}\).
- To convert it:
\[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]

2. **Convert \(40 \frac{1}{2}\)**:
- The whole number part is 40 and the fractional part is \(\frac{1}{2}\).
- To convert it:
\[ 40 \frac{1}{2} = \frac{40 \times 2 + 1}{2} = \frac{80 + 1}{2} = \frac{81}{2} \]

### Step 2: Calculate the Cost
Now that we have both values as improper fractions, we can calculate the cost.

- The cost per metre is \(\frac{81}{2}\) and the length is \(\frac{10}{3}\).
- To find the total cost:
\[ \text{Total Cost} = \text{Length} \times \text{Cost per metre} = \frac{10}{3} \times \frac{81}{2} \]

### Step 3: Multiply the Fractions
Now we multiply the fractions:
\[ \frac{10 \times 81}{3 \times 2} = \frac{810}{6} \]

### Step 4: Simplify the Result
Now we simplify \(\frac{810}{6}\):
\[ \frac{810 \div 6}{6 \div 6} = \frac{135}{1} = 135 \]

### Conclusion
Thus, the total cost of \(3 \frac{1}{3}\) metres of cloth at Rs \(40 \frac{1}{2}\) per metre is **Rs 135**.

---