The cost of `7(2)/(5)`metres of ribbon is Rs. `12(3)/(8)`., find its cost per metre..

Options

A. Rs.2.67
B. Rs.1.67
C. Rs.2.05
D. Rs.1.04

Answer

To find the cost per metre of the ribbon, we will follow these steps:

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

1. **Convert 7 \( \frac{2}{5} \)** to an improper fraction:
- Multiply the whole number (7) by the denominator (5) and add the numerator (2).
- \( 7 \times 5 + 2 = 35 + 2 = 37 \)
- Therefore, \( 7 \frac{2}{5} = \frac{37}{5} \).

2. **Convert 12 \( \frac{3}{8} \)** to an improper fraction:
- Multiply the whole number (12) by the denominator (8) and add the numerator (3).
- \( 12 \times 8 + 3 = 96 + 3 = 99 \)
- Therefore, \( 12 \frac{3}{8} = \frac{99}{8} \).

### Step 2: Set up the equation to find the cost per metre.

- We know that the cost of \( \frac{37}{5} \) metres of ribbon is \( \frac{99}{8} \) rupees.
- To find the cost per metre, we will divide the total cost by the total length in metres:
\[ \text{Cost per metre} = \frac{\text{Total Cost}}{\text{Total Length}} = \frac{\frac{99}{8}}{\frac{37}{5}} \]

### Step 3: Simplify the division of fractions.

- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{99}{8} \div \frac{37}{5} = \frac{99}{8} \times \frac{5}{37} \]

### Step 4: Multiply the fractions.

- Multiply the numerators and the denominators:
\[ \frac{99 \times 5}{8 \times 37} = \frac{495}{296} \]

### Step 5: Calculate the decimal value.

- To find the cost per metre, we will divide 495 by 296:
\[ 495 \div 296 \approx 1.67 \text{ rupees} \]

### Final Answer:
The cost per metre of the ribbon is approximately Rs. 1.67.

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