The price of `4 (1)/(2)` m of cloth is Rs. `60 (3)/(4)`. Find the cost per meter.
A. `15 (1)/(2)`
B. `13 (1)/(2)`
C. `14(3)/(4)`
D. `13 (3)/(4)`

Options

A. D
B. C
C. B
D. A

Answer

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

### Step 1: Convert the mixed numbers to improper fractions
The price of 4 \( \frac{1}{2} \) meters of cloth can be converted to an improper fraction:
\[ 4 \frac{1}{2} = 4 \times 2 + 1 = 8 + 1 = \frac{9}{2} \text{ meters} \]

The cost of the cloth is given as Rs. \( 60 \frac{3}{4} \):
\[ 60 \frac{3}{4} = 60 \times 4 + 3 = 240 + 3 = \frac{243}{4} \text{ Rs.} \]

### Step 2: Set up the equation for cost per meter
To find the cost per meter, we need to divide the total cost by the total meters:
\[ \text{Cost per meter} = \frac{\text{Total Cost}}{\text{Total Meters}} = \frac{\frac{243}{4}}{\frac{9}{2}} \]

### Step 3: Divide the fractions
When dividing fractions, we multiply by the reciprocal of the second fraction:
\[ \frac{\frac{243}{4}}{\frac{9}{2}} = \frac{243}{4} \times \frac{2}{9} \]

### Step 4: Simplify the multiplication
Now, we can simplify:
\[ = \frac{243 \times 2}{4 \times 9} = \frac{486}{36} \]

### Step 5: Simplify the fraction
Now, we simplify \( \frac{486}{36} \):
\[ = \frac{486 \div 18}{36 \div 18} = \frac{27}{2} \]

### Step 6: Convert to a mixed number
Now, we convert \( \frac{27}{2} \) to a mixed number:
\[ 27 \div 2 = 13 \text{ remainder } 1 \Rightarrow 13 \frac{1}{2} \]

### Conclusion
Thus, the cost per meter of cloth is Rs. \( 13 \frac{1}{2} \).

### Final Answer
The correct option is **B. \( 13 \frac{1}{2} \)**.

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