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Percentage and its Applications - Finding Increase or Decrease Percent

Grade 8ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Original Value (Base): The original value is the quantity before any change happens. It serves as the reference point for calculations. Visually, imagine this as a full bar in a bar graph or a starting point on a number line.

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Increase: An increase happens when the final value is greater than the original value. This can be visualized as an upward-pointing arrow or an additional block added to the top of the original bar, representing growth.

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Decrease: A decrease happens when the final value is less than the original value. Visually, this is represented by a downward-pointing arrow or a portion of the original bar being shaded out or removed.

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Amount of Change: This is the absolute difference between the new value and the original value. It represents the 'gap' between the two heights on a comparison chart, regardless of whether it went up or down.

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Percentage as a Ratio: The percentage increase or decrease is the ratio of the change to the original value, expressed as a fraction of 100. It tells us how much the value changed for every 100 units of the original amount.

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Unit Uniformity: When calculating changes, both the change and the original value must be in the same units. For example, if comparing weights, both must be in kgkg or both in gg before applying the percentage formula.

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The 100% Benchmark: The original value is always considered as 100%100\%. If there is a 20%20\% increase, the new value becomes 120%120\% (100%+20%100\% + 20\%) of the original. If there is a 20%20\% decrease, the new value becomes 80%80\% (100%−20%100\% - 20\%) of the original.

📐Formulae

Increase=New Value−Original Value\text{Increase} = \text{New Value} - \text{Original Value}

Decrease=Original Value−New Value\text{Decrease} = \text{Original Value} - \text{New Value}

Percentage Increase=(IncreaseOriginal Value×100)%\text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Original Value}} \times 100 \right) \%

Percentage Decrease=(DecreaseOriginal Value×100)%\text{Percentage Decrease} = \left( \frac{\text{Decrease}}{\text{Original Value}} \times 100 \right) \%

New Value=Original Value×(1+Percentage Increase100)\text{New Value} = \text{Original Value} \times \left( 1 + \frac{\text{Percentage Increase}}{100} \right)

New Value=Original Value×(1−Percentage Decrease100)\text{New Value} = \text{Original Value} \times \left( 1 - \frac{\text{Percentage Decrease}}{100} \right)

💡Examples

Problem 1:

The price of a motorcycle increased from Rs 50,000 to Rs 55,000. Calculate the percentage increase in the price.

Solution:

  1. Identify the values: Original Value=Rs 50,000\text{Original Value} = \text{Rs } 50,000 and New Value=Rs 55,000\text{New Value} = \text{Rs } 55,000\2. Find the Increase: Increase=55,000−50,000=Rs 5,000\text{Increase} = 55,000 - 50,000 = \text{Rs } 5,000\3. Apply the formula: Percentage Increase=(5,00050,000×100)%\text{Percentage Increase} = \left( \frac{5,000}{50,000} \times 100 \right) \%\4. Simplify: Percentage Increase=(110×100)%=10%\text{Percentage Increase} = \left( \frac{1}{10} \times 100 \right) \% = 10 \%

Explanation:

To find the percentage increase, we first determine the actual amount of the price hike (Rs 5,000) and then calculate what percent this increase is of the starting price (Rs 50,000).

Problem 2:

The population of a small town was 8,000. Due to migration, it decreased to 7,200. Find the percentage decrease in the population.

Solution:

  1. Identify the values: Original Value=8,000\text{Original Value} = 8,000 and New Value=7,200\text{New Value} = 7,200\2. Find the Decrease: Decrease=8,000−7,200=800\text{Decrease} = 8,000 - 7,200 = 800\3. Apply the formula: Percentage Decrease=(8008,000×100)%\text{Percentage Decrease} = \left( \frac{800}{8,000} \times 100 \right) \%\4. Simplify: Percentage Decrease=(110×100)%=10%\text{Percentage Decrease} = \left( \frac{1}{10} \times 100 \right) \% = 10 \%

Explanation:

The percentage decrease is found by dividing the reduction in population (800) by the original population (8,000) and then multiplying by 100 to convert the fraction into a percentage.