Shortcut Trick
Let the original fraction be 100/100 = 1.
New Numerator = 100 − 25 = 75
New Denominator = 100 + 25 = 125
New Fraction = 75 ÷ 125 = 3/5 = 0.6 (which is 60% of the original).
Percentage decrease = (1 − 0.6) × 100% = 40%.
∴ The correct answer is 40%.
Alternate Method
Given:
The numerator of a fraction is decreased by 25%.
The denominator of the fraction is increased by 25%.
Formula Used:
Percentage Decrease = [(Original Value − New Value) ÷ Original Value] × 100%
Calculations:
Original Fraction = 100%
New Fraction = 60%
Decrease = 40%
Decrease = 100% − 60% = 40%
⇒ Let the original fraction be x / y.
⇒ New Numerator = x − (25/100) × x = 0.75x
⇒ New Denominator = y + (25/100) × y = 1.25y
⇒ New Fraction = 0.75x ÷ 1.25y = (75 ÷ 125) × (x / y) = 3/5 × (x / y)
⇒ Decrease in fraction = (x / y) − [3/5 × (x / y)] = 2/5 × (x / y)
⇒ Percentage decrease = [{2/5 × (x / y)} ÷ (x / y)] × 100%
⇒ Percentage decrease = 2/5 × 100% = 40%
∴ The correct answer is 40%.
Additional Information
Percentage Change
Percentage change is calculated as [(Final Value − Initial Value) ÷ Initial Value] × 100. A negative result indicates a decrease, while a positive result indicates an increase.
Successive Percentage Change
When a value is sequentially changed by x% and then by y%, the net percentage change can also be found using the effective formula: Net Change = x + y + (x × y) ÷ 100.
Fraction to Percentage Conversion
To convert a fraction into a percentage, multiply it by 100. For example, the fraction 3/5 expressed as a percentage is 3/5 × 100% = 60%. Therefore, any value that drops to 60% of its original has observed a 40% reduction.