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John earns 33.33% more than Peter. By what percentage is Peter's earning less than that of John's?

Question

John earns 33.33% more than Peter.

By what percentage is Peter's earning less than that of John's?

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Solution

Let's solve the problem step by step.

  1. Let's assume Peter's earnings are P P .

  2. John earns 33.33% more than Peter. Therefore, John's earnings can be calculated as: J=P+0.3333P=1.3333P J = P + 0.3333P = 1.3333P

  3. We need to find by what percentage Peter's earnings are less than John's. To do this, we calculate the difference between John's and Peter's earnings: Difference=JP=1.3333PP=0.3333P \text{Difference} = J - P = 1.3333P - P = 0.3333P

  4. To find the percentage by which Peter's earnings are less than John's, we use the formula: Percentage=(DifferenceJ)×100 \text{Percentage} = \left( \frac{\text{Difference}}{J} \right) \times 100

  5. Substituting the values we have: Percentage=(0.3333P1.3333P)×100 \text{Percentage} = \left( \frac{0.3333P}{1.3333P} \right) \times 100

  6. Simplifying the fraction: Percentage=(0.33331.3333)×100 \text{Percentage} = \left( \frac{0.3333}{1.3333} \right) \times 100

  7. Calculating the division: Percentage=0.25×100 \text{Percentage} = 0.25 \times 100

  8. Finally: Percentage=25% \text{Percentage} = 25\%

So, Peter's earnings are 25% less than John's.

This problem has been solved

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