Find the percentage increase in each of the following: (a) Increase 50 by 5. (b) Increase from 20 to 25. (c) Increase 40 cm by 12 cm. (d) Increase from $48 to $108.
Understand the Problem
The question asks to calculate the percentage increase for various scenarios. This involves finding the difference between the new and original values, dividing by the original value, and then multiplying by 100 to express the result as a percentage.
Answer
(a) 10% (b) 25% (c) 30% (d) 125%
Answer for screen readers
(a) 10% (b) 25% (c) 30% (d) 125%
Steps to Solve
- Calculate the percentage increase for (a)
To find the percentage increase when 50 is increased by 5, we first determine the increase, which is 5. Then, we divide this increase by the original value (50) and multiply by 100 to express it as a percentage
$Percentage\ Increase = \frac{Increase}{Original\ Value} \times 100$
$Percentage\ Increase = \frac{5}{50} \times 100$
$Percentage\ Increase = 0.1 \times 100 = 10%$
- Calculate the percentage increase for (b)
To find the percentage increase from 20 to 25, we first determine the increase, which is $25 - 20 = 5$. Then, we divide this increase by the original value (20) and multiply by 100 to express it as a percentage.
$Percentage\ Increase = \frac{Increase}{Original\ Value} \times 100$
$Percentage\ Increase = \frac{5}{20} \times 100$
$Percentage\ Increase = 0.25 \times 100 = 25%$
- Calculate the percentage increase for (c)
To find the percentage increase when 40 cm is increased by 12 cm, we first determine the increase, which is 12 cm. Then, we divide this increase by the original value (40 cm) and multiply by 100 to express it as a percentage.
$Percentage\ Increase = \frac{Increase}{Original\ Value} \times 100$
$Percentage\ Increase = \frac{12}{40} \times 100$
$Percentage\ Increase = 0.3 \times 100 = 30%$
- Calculate the percentage increase for (d)
To find the percentage increase from $48 to $108, we first determine the increase, which is $108 - $48 = $60. Then, we divide this increase by the original value ($48) and multiply by 100 to express it as a percentage.
$Percentage\ Increase = \frac{Increase}{Original\ Value} \times 100$
$Percentage\ Increase = \frac{60}{48} \times 100$
$Percentage\ Increase = 1.25 \times 100 = 125%$
(a) 10% (b) 25% (c) 30% (d) 125%
More Information
Percentage increase is a way to express the relative change in a quantity. It is particularly useful for comparing changes in different quantities or over different periods.
Tips
A common mistake is to divide by the new value instead of the original value when calculating the percentage increase. It's important to always use the original value as the denominator in the calculation. Another mistake is forgetting to multiply by 100 to express the answer as a percentage.
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