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Solve the following problems related to profit and loss: 1. If the cost price is Gh¢12.50 and the profit is 30%, what is the selling price? 2. If the selling price is Gh¢20.00 and the profit is 25%, w

Mathematics

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Here are the solutions to problems 1 to 6.

1.

  1. Identify the given values.

    Cost Price (CP) = Gh¢12.50
    Profit percentage = 30% = 0.30

  2. Calculate the Selling Price (SP).

    SP=CP×(1+Profit Percentage)SP = CP \times (1 + \text{Profit Percentage}) SP=Gh¢12.50×(1+0.30)SP = \text{Gh¢}12.50 \times (1 + 0.30) SP=Gh¢12.50×1.30SP = \text{Gh¢}12.50 \times 1.30 SP=Gh¢16.25SP = \text{Gh¢}16.25

    The selling price was Gh¢16.25\boxed{\text{Gh¢}16.25}.

    2.

  3. Identify the given values.

    Selling Price (SP) = Gh¢20.00
    Profit percentage = 25% = 0.25

  4. Calculate the Cost Price (CP).

    CP=SP1+Profit PercentageCP = \frac{SP}{1 + \text{Profit Percentage}} CP=Gh¢20.001+0.25CP = \frac{\text{Gh¢}20.00}{1 + 0.25} CP=Gh¢20.001.25CP = \frac{\text{Gh¢}20.00}{1.25} CP=Gh¢16.00CP = \text{Gh¢}16.00

    The cost price of the article was Gh¢16.00\boxed{\text{Gh¢}16.00}.

    3.

  5. Identify the given values.

    Selling Price (SP) = Gh¢300
    Profit percentage = 20% = 0.20

  6. Calculate the Cost Price (CP).

    CP=SP1+Profit PercentageCP = \frac{SP}{1 + \text{Profit Percentage}} CP=Gh¢3001+0.20CP = \frac{\text{Gh¢}300}{1 + 0.20} CP=Gh¢3001.20CP = \frac{\text{Gh¢}300}{1.20} CP=Gh¢250CP = \text{Gh¢}250

    The cost price was Gh¢250\boxed{\text{Gh¢}250}.

    4.

  7. Identify the given values.

    Cost Price (CP) = Gh¢15,000.00
    Profit percentage = 20% = 0.20

  8. Calculate the Selling Price (SP).

    SP=CP×(1+Profit Percentage)SP = CP \times (1 + \text{Profit Percentage}) SP=Gh¢15,000.00×(1+0.20)SP = \text{Gh¢}15,000.00 \times (1 + 0.20) SP=Gh¢15,000.00×1.20SP = \text{Gh¢}15,000.00 \times 1.20 SP=Gh¢18,000.00SP = \text{Gh¢}18,000.00

    His selling price was Gh¢18,000.00\boxed{\text{Gh¢}18,000.00}.

    5.

  9. Identify the given values.

    Cost Price (CP) = Gh¢8,500
    Selling Price (SP) = Gh¢9,500

  10. Calculate the profit.

    Profit=SP−CP\text{Profit} = SP - CP Profit=Gh¢9,500−Gh¢8,500\text{Profit} = \text{Gh¢}9,500 - \text{Gh¢}8,500 Profit=Gh¢1,000\text{Profit} = \text{Gh¢}1,000

  11. Calculate the percentage gain.

    Percentage Gain=ProfitCP×100%\text{Percentage Gain} = \frac{\text{Profit}}{CP} \times 100\% Percentage Gain=Gh¢1,000Gh¢8,500×100%\text{Percentage Gain} = \frac{\text{Gh¢}1,000}{\text{Gh¢}8,500} \times 100\% Percentage Gain=10008500×100%\text{Percentage Gain} = \frac{1000}{8500} \times 100\% Percentage Gain=217×100%\text{Percentage Gain} = \frac{2}{17} \times 100\% Percentage Gain≈11.7647%\text{Percentage Gain} \approx 11.7647\%

    His percentage gain was approximately 11.76%\boxed{11.76\%}.

    6.

  12. Calculate the total revenue from each batch of boxes.

    Revenue from 100 boxes:

    R1=100 boxes×80 Gp/box=8000 GpR_1 = 100 \text{ boxes} \times 80 \text{ Gp/box} = 8000 \text{ Gp}

    Revenue from 800 boxes:

    R2=800 boxes×60 Gp/box=48000 GpR_2 = 800 \text{ boxes} \times 60 \text{ Gp/box} = 48000 \text{ Gp}

    Revenue from 600 boxes:

    R3=600 boxes×40 Gp/box=24000 GpR_3 = 600 \text{ boxes} \times 40 \text{ Gp/box} = 24000 \text{ Gp}

  13. Calculate the total number of boxes sold.

    Total Boxes=100+800+600=1500 boxes\text{Total Boxes} = 100 + 800 + 600 = 1500 \text{ boxes}

  14. Calculate the total revenue.

    Total Revenue=R1+R2+R3\text{Total Revenue} = R_1 + R_2 + R_3 Total Revenue=8000 Gp+48000 Gp+24000 Gp\text{Total Revenue} = 8000 \text{ Gp} + 48000 \text{ Gp} + 24000 \text{ Gp} Total Revenue=80000 Gp\text{Total Revenue} = 80000 \text{ Gp}

  15. Calculate the average selling price per box.

    Average Selling Price per Box=Total RevenueTotal Boxes\text{Average Selling Price per Box} = \frac{\text{Total Revenue}}{\text{Total Boxes}} Average Selling Price per Box=80000 Gp1500 boxes\text{Average Selling Price per Box} = \frac{80000 \text{ Gp}}{1500 \text{ boxes}} Average Selling Price per Box=80015 Gp/box\text{Average Selling Price per Box} = \frac{800}{15} \text{ Gp/box} Average Selling Price per Box=1603 Gp/box\text{Average Selling Price per Box} = \frac{160}{3} \text{ Gp/box} Average Selling Price per Box≈53.33 Gp/box\text{Average Selling Price per Box} \approx 53.33 \text{ Gp/box}

    The average selling price per box was approximately 53.33 Gp\boxed{53.33 \text{ Gp}}.

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