The cost of `3(1)/(2)` metres of cloth is Rs. `166(1)/(4)`. What is the cost of one metre of cloth?

Answer

To find the cost of one metre of cloth when the cost of \(3\frac{1}{2}\) metres is \(Rs. 166\frac{1}{4}\), we can follow these steps:

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

**For \(3\frac{1}{2}\):**
\[ 3\frac{1}{2} = 3 \times 2 + 1 = 6 + 1 = \frac{7}{2} \]

**For \(166\frac{1}{4}\):**
\[ 166\frac{1}{4} = 166 \times 4 + 1 = 664 + 1 = \frac{665}{4} \]

### Step 2: Set up the equation for the cost of one metre
Now that we have the costs in improper fractions, we can set up the equation to find the cost of one metre of cloth.

Let the cost of one metre of cloth be \(x\). Therefore, the cost of \(3\frac{1}{2}\) metres can be expressed as:
\[ \frac{7}{2}x = \frac{665}{4} \]

### Step 3: Solve for \(x\)
To find \(x\), we will multiply both sides of the equation by the reciprocal of \(\frac{7}{2}\), which is \(\frac{2}{7}\):
\[ x = \frac{665}{4} \times \frac{2}{7} \]

### Step 4: Simplify the expression
Now, we can simplify the expression:
\[ x = \frac{665 \times 2}{4 \times 7} = \frac{1330}{28} \]

### Step 5: Further simplify the fraction
Next, we can simplify \(\frac{1330}{28}\):
\[ \frac{1330 \div 14}{28 \div 14} = \frac{95}{2} \]

### Step 6: Convert to decimal
Finally, we can convert \(\frac{95}{2}\) to a decimal:
\[ \frac{95}{2} = 47.5 \]

### Conclusion
Thus, the cost of one metre of cloth is \(Rs. 47.5\).

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