Answer :

To find the cost per metre of the rope, we need to divide the total cost by the total number of metres.

The cost of 7 [tex]\frac{2}{3}[/tex] metres of rope is ₹12 [tex]\frac{3}{4}[/tex]. We need to convert these mixed numbers into improper fractions to make the division easier.

  1. Convert 7 [tex]\frac{2}{3}[/tex] to an improper fraction:

    • [tex]7 \frac{2}{3} = \frac{3 \times 7 + 2}{3} = \frac{21 + 2}{3} = \frac{23}{3}[/tex]

  2. Convert 12 [tex]\frac{3}{4}[/tex] to an improper fraction:

    • [tex]12 \frac{3}{4} = \frac{4 \times 12 + 3}{4} = \frac{48 + 3}{4} = \frac{51}{4}[/tex]

Now we divide the total cost by the total length to find the cost per metre:

[tex]\text{Cost per metre} = \frac{\frac{51}{4}}{\frac{23}{3}}[/tex]

To divide fractions, multiply by the reciprocal of the divisor:

[tex]\text{Cost per metre} = \frac{51}{4} \times \frac{3}{23}[/tex]

  1. Simplify by multiplying the numerators and denominators:
    • [tex]\frac{51 \times 3}{4 \times 23} = \frac{153}{92}[/tex]

Finally, convert the improper fraction [tex]\frac{153}{92}[/tex] into a mixed number:

  1. Divide 153 by 92 to find the quotient and remainder:
    • Quotient is 1 and remainder is 61, so [tex]\frac{153}{92} = 1 \frac{61}{92}[/tex]

Therefore, the cost per metre of the rope is approximately ₹1 [tex]\frac{61}{92}[/tex].

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