Math Problem Statement

Company A was running at a loss of 2lakhs in FY 2023. This is 10% of the revenue. Next year company wants to gain a profit of 20%, What should be final revenue for nest year?

Solution

To calculate the final revenue for the next year, we can follow these steps:

  1. Current Year Loss and Revenue:
    In FY 2023, the company had a loss of ₹2,00,000, which represents 10% of the revenue.
    Therefore, the revenue in FY 2023 is:

    Revenue for FY 2023=2,00,0000.10=20,00,000\text{Revenue for FY 2023} = \frac{2,00,000}{0.10} = ₹20,00,000

  2. Profit Target for Next Year:
    The company wants to make a profit of 20% in the next year.
    This means the company aims to have its revenue cover both the expenses (i.e., last year's revenue since they were running at a 10% loss) and an additional 20% profit on top of that.

    Let Rnext yearR_{\text{next year}} be the required revenue for the next year.

    • The expenses will still be ₹20,00,000.
    • The desired profit is 20% of this revenue, or 0.20×Rnext year0.20 \times R_{\text{next year}}.
  3. Revenue Equation:
    To achieve a profit of 20%, the revenue should cover both the expenses and the profit:

    Rnext year=20,00,000+0.20×Rnext yearR_{\text{next year}} = 20,00,000 + 0.20 \times R_{\text{next year}}

  4. Solving for Rnext yearR_{\text{next year}}:
    Rearranging the equation:

    Rnext year0.20×Rnext year=20,00,000R_{\text{next year}} - 0.20 \times R_{\text{next year}} = 20,00,000

    0.80×Rnext year=20,00,0000.80 \times R_{\text{next year}} = 20,00,000

    Rnext year=20,00,0000.80=25,00,000R_{\text{next year}} = \frac{20,00,000}{0.80} = ₹25,00,000

Therefore, the company needs a revenue of ₹25,00,000 in the next year to achieve a 20% profit.


Would you like more details on the solution or any specific part? Here are 5 related questions to think about:

  1. What would be the revenue target if the company wanted a 30% profit instead?
  2. How would the target change if the company had a larger loss percentage, say 15%?
  3. What would be the expenses next year if the company achieves its target revenue of ₹25,00,000?
  4. How can changes in costs impact the required revenue for the desired profit?
  5. What strategies can a company use to increase revenue to meet profit targets?

Tip: Always ensure to include fixed costs and variable costs when projecting future revenues to meet profit goals.

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Math Problem Analysis

Mathematical Concepts

Algebra
Percentage
Revenue Calculation

Formulas

Revenue = Loss / Percentage Loss
Required Revenue = Expenses + Desired Profit
0.80 * Required Revenue = Expenses

Theorems

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Suitable Grade Level

Grades 9-12