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The value of (3)/(2) x (1)/(2) / (3)/(2) ; 20) An aeroplane covers a distance of 300 Km in 5 hrs.

Mathematics

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Step-by-step solution

7 steps

19) The value of 32×12÷32\frac{3}{2} \times \frac{1}{2} \div \frac{3}{2}

  1. Perform the multiplication from left to right.

    32×12=3×12×2=34\frac{3}{2} \times \frac{1}{2} = \frac{3 \times 1}{2 \times 2} = \frac{3}{4}
  2. Perform the division.

    To divide by a fraction, multiply by its reciprocal.

    34÷32=34×23\frac{3}{4} \div \frac{3}{2} = \frac{3}{4} \times \frac{2}{3}
  3. Multiply the fractions.

    3×24×3=612\frac{3 \times 2}{4 \times 3} = \frac{6}{12}
  4. Simplify the fraction.

    612=12\frac{6}{12} = \frac{1}{2}

    The options provided are A. 1, B. #, C. 100, D. 11, E. 12. None of the options match the calculated value of 12\frac{1}{2}.

    The value is 12\boxed{\frac{1}{2}}.

    20) An aeroplane covers a distance of 300 Km in 5 hrs.

  5. Recall the formula for average speed.

    Average Speed=DistanceTime\text{Average Speed} = \frac{\text{Distance}}{\text{Time}}
  6. Substitute the given values into the formula.

    Distance=300 Km\text{Distance} = 300 \text{ Km} Time=5 hrs\text{Time} = 5 \text{ hrs} Average Speed=300 Km5 hrs\text{Average Speed} = \frac{300 \text{ Km}}{5 \text{ hrs}}
  7. Calculate the average speed.

    Average Speed=60 Km/h\text{Average Speed} = 60 \text{ Km/h}

    Comparing this to the given options:
    A. 35 Km/h
    B. 40 Km/h
    C. 50 Km/h
    D. 60 Km/h
    E. 65 Km/h

    The calculated average speed matches option D.

    The average speed of the aeroplane is D. 60 Km/h\boxed{\text{D. } 60 \text{ Km/h}}.

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