Shortcut Trick
Apply the successive percentage formula: Net % Change = x + y + (xy ÷ 100).
Here, Sonu is 30% more than Monu (x = 30) and Sunny is 15% more than Sonu (y = 15).
Net percentage increase = 30 + 15 + (30 × 15 ÷ 100)
Net percentage increase = 45 + 4.5 = 49.5%.
∴ The correct answer is 49.5 percent.
Alternate Method
Given:
Sunny’s income = Sonu’s income + 15%
Sonu’s income = Monu’s income + 30%
Let the income of Monu be 100.
⇒ Sonu’s income = 100 + (30% of 100)
⇒ Sonu’s income = 100 + 30 = 130
⇒ Sunny’s income = 130 + (15% of 130)
⇒ Sunny’s income = 130 + (15 × 130 ÷ 100) = 130 + 19.5
⇒ Sunny’s income = 149.5
⇒ Required Percentage = Sunny’s income − Monu’s income
⇒ Required Percentage = 149.5 − 100 = 49.5%
∴ The correct answer is 49.5 percent.
Additional Information
Successive Percentage Change
When a value is increased by x% and then again by y%, the net percentage change is given by the formula [x + y + (xy ÷ 100)]%.
Base Selection Rule
In comparative percentage problems, it is always easier to assume the base value (the value being compared to) as 100 to simplify calculations.
Percentage Difference
The formula for % more is [(Higher Value − Lower Value) ÷ Lower Value] × 100, where the 'Lower Value' is the reference point (Monu in this case).