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Calculate the percentage profit given CP=12,000 and SP=14,400. Also, calculate the map distance if the actual distance is 10 km and the scale is 1:25000.

Mathematics

ScanSolve AI Answer

Answer

20%20\%

40 cm40 \text{ cm}

Step-by-step solution

6 steps

I've deciphered the questions from the image. Here are the solutions:

: Percentage profit

  1. Identify the cost price and selling price.

    Cost Price (CPCP) = 12,000/=12,000/=
    Selling Price (SPSP) = 14,400/=14,400/=

  2. Calculate the profit.

    Profit = SP−CPSP - CP
    Profit = 14,400−12,00014,400 - 12,000
    Profit = 2,400/=2,400/=

  3. Calculate the percentage profit.

    Percentage Profit = ProfitCP×100%\frac{\text{Profit}}{CP} \times 100\%
    Percentage Profit = 2,40012,000×100%\frac{2,400}{12,000} \times 100\%
    Percentage Profit = 24120×100%\frac{24}{120} \times 100\%
    Percentage Profit = 15×100%\frac{1}{5} \times 100\%
    Percentage Profit = 20%20\%
    The percentage profit is 20%\boxed{20\%}.

    : Map distance

  4. Understand the given scale and actual distance.

    The map scale is 1:250001:25000. This means 1 unit1 \text{ unit} on the map represents 25000 units25000 \text{ units} in actual distance.
    The actual distance between two towns is 10 km10 \text{ km}.

  5. Convert the actual distance to centimeters.

    We know that 1 km=1000 m1 \text{ km} = 1000 \text{ m} and 1 m=100 cm1 \text{ m} = 100 \text{ cm}.
    So, 1 km=1000×100 cm=100,000 cm1 \text{ km} = 1000 \times 100 \text{ cm} = 100,000 \text{ cm}.
    Actual distance = 10 km=10×100,000 cm=1,000,000 cm10 \text{ km} = 10 \times 100,000 \text{ cm} = 1,000,000 \text{ cm}.

  6. Calculate the distance on the map.

    Map distance = Actual distanceScale factor\frac{\text{Actual distance}}{\text{Scale factor}}
    Map distance = 1,000,000 cm25000\frac{1,000,000 \text{ cm}}{25000}
    Map distance = 100025 cm\frac{1000}{25} \text{ cm}
    Map distance = 40 cm40 \text{ cm}
    The distance on the map is 40 cm\boxed{40 \text{ cm}}.

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