High School

1. If 12 trousers of equal size can be prepared in 27 metres of cloth, what length of cloth is required for each trouser?

2. From a rope 45 metres long, pieces of equal size are cut, each measuring 3 3/4 metres. How many pieces are cut off?

3. The cost of 2 3/4 metres of cloth is 146 2/3. Find the cost of cloth per metre.

4. From a rope 48 1/2 metre long, as many pieces each 3 3/4 metre long as possible are cut off. Find how many pieces can be cut off and what fraction is left?

Answer :

Let's break down each question step-by-step:

  1. Finding the cloth length for each trouser:

    • To find the length of cloth required for each trouser, we need to divide the total length of cloth by the number of trousers.
    • If 12 trousers require 27 meters of cloth, then for 1 trouser, the calculation is:
    • [tex]\text{Length of cloth per trouser} = \frac{27 \text{ meters}}{12} = 2.25 \text{ meters}[/tex]
    • Therefore, each trouser requires 2.25 meters of cloth.

  2. Calculating number of pieces from a rope:

    • From a 45 meters long rope, pieces of 3 3/4 meters each are cut.
    • First, convert 3 3/4 into an improper fraction or a decimal: [tex]3 3/4 = \frac{15}{4} = 3.75 \, \text{meters}[/tex].
    • To find out how many such pieces can be cut, divide the total length by the length of each piece:
    • [tex]\text{Number of pieces} = \frac{45}{3.75} = 12[/tex]
    • So, 12 pieces, each 3 3/4 meters long, can be cut off.

  3. Calculating cost per meter of cloth:

    • The cost given is for 2 3/4 meters of cloth as 146 2/3.
    • First, convert both into improper fractions or decimals:
      • [tex]2 3/4 = \frac{11}{4} \, \text{meters}[/tex]
      • [tex]146 2/3 = \frac{440}{3}[/tex]
    • To find the cost per meter, divide the total cost by the quantity:
    • [tex]\text{Cost per meter} = \frac{\frac{440}{3}}{\frac{11}{4}} = \frac{440 \times 4}{3 \times 11} = \frac{1760}{33} \approx 53.33[/tex]
    • Therefore, the cost of cloth per meter is approximately 53.33.

  4. Finding how many pieces can be cut from a rope and fraction left:

    • The rope is 48 1/2 meters long, and pieces are each 3 3/4 meters.
    • Convert measurements to improper fractions or decimals:
      • [tex]48 1/2 = \frac{97}{2} = 48.5 \, \text{meters}[/tex]
      • [tex]3 3/4 = \frac{15}{4} = 3.75 \, \text{meters}[/tex]
    • Calculate the number of complete pieces that can be cut:
    • [tex]\text{Number of pieces} = \frac{48.5}{3.75} \approx 12[/tex]
    • To find the fraction of the rope left, calculate the total length of the 12 pieces and subtract from the original length:
    • [tex]12 \times 3.75 = 45 \text{ meters}[/tex]
    • Fraction left = original length - length of used rope:
    • [tex]\text{Fraction left} = 48.5 - 45 = 3.5 \text{ meters}[/tex]
    • So, 12 pieces can be cut off and 3.5 meters of rope will be left.

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