If the cost of 6 `1/4` m of cloth is Rs 1421 `7/8` then find the cost of 1 metre of cloth

Answer

To find the cost of 1 metre of cloth given that the cost of 6 `1/4` m of cloth is Rs 1421 `7/8`, we will follow these steps:

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

**For the cloth length:**
- The mixed number is \(6 \frac{1}{4}\).
- To convert it:
\[ 6 \frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4} \]

**For the cost:**
- The mixed number is \(1421 \frac{7}{8}\).
- To convert it:
\[ 1421 \frac{7}{8} = \frac{1421 \times 8 + 7}{8} = \frac{11368 + 7}{8} = \frac{11375}{8} \]

### Step 2: Calculate the Cost of 1 Metre of Cloth
Now, we need to find the cost of 1 metre of cloth. The formula to find the cost per metre is:
\[ \text{Cost of 1 m} = \frac{\text{Total Cost}}{\text{Total Length}} \]

Substituting the values we found:
\[ \text{Cost of 1 m} = \frac{\frac{11375}{8}}{\frac{25}{4}} \]

### Step 3: Simplify the Expression
To divide fractions, we multiply by the reciprocal:
\[ \text{Cost of 1 m} = \frac{11375}{8} \times \frac{4}{25} \]

### Step 4: Perform the Multiplication
Now we can multiply the fractions:
\[ \text{Cost of 1 m} = \frac{11375 \times 4}{8 \times 25} \]

### Step 5: Simplify the Result
Calculating the denominator:
\[ 8 \times 25 = 200 \]
Now, we can simplify the fraction:
\[ \text{Cost of 1 m} = \frac{11375 \times 4}{200} \]

Calculating \(11375 \times 4\):
\[ 11375 \times 4 = 45500 \]

So we have:
\[ \text{Cost of 1 m} = \frac{45500}{200} \]

### Step 6: Final Division
Now, we divide:
\[ \text{Cost of 1 m} = 227.5 \]

Thus, the cost of 1 metre of cloth is **Rs 227.5**.

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