Percentage Increase
To increase a quantity by a percentage find the percentage of the quantity and add it to the original quantity.
Example 1: Increase 320 by 20%.
Solution. 20% of 320 = \(\frac{ 20}{ 100}\) x 320 = 64
Therefore, Increased amount = Rs 320 + Rs 64 = Rs 384.
Percentage Decrease
To decrease a quantity by a percentage, find the percentage of the quantity and subtract it from the original quantity.
Example 2: Decrease 120 by \(12\frac{1}{2}\) %.
Solution. \(12\frac{1}{2}\)% of 120
= Rs \(\frac{ 12.5}{ 100}\) of 120
= Rs \(\frac{ 125 }{ 10 * 100}\) x 120
= Rs 15
Therefore, Decreased amount = Rs 120 — Rs15 = Rs 105.
Percentage Change
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Percentage change = ( \(\frac{ Actual change (Increase or Decrease)}{ Original quantity}\) x 100) % |
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Percentage error = (\(\frac{ Error}{Actual Value}\) x 100) % |
Example 3: Sabita’s weight decreased from 80 kg to 40 kg. Find the percentage decrease.
Solution. Decrease in weight = (80 — 40) kg = 40 kg.
Therefore, % decrease = \(\frac{ 40}{ 80}\) x100% = 50%.
Example 4: The distance between two places was 200 km. It was measured as 300 km. Find the percentage error.
Solution. Error = 300 km — 200 km = 100 km.
Therefore, %error = \(\frac{ error}{ actual value}\) x 100%
= \(\frac{ 100}{ 200}\) x 100 = 50%.