The correct option is (b) - 30% increase.
[as per provisional answerkey]Solution
Let the initial monthly salary of the person be 100 units.
Initial Savings = 10% of 100 = 10 units.
Initial Expenditure = Salary - Savings = 100−10=90 units.
New Scenario:
New Salary = Initial Salary + 12% increase = 100+12=112 units.
New Expenditure = Initial Expenditure + 10% increase = 90 + (10% of 90) = 90+9=99 units.
Calculating New Savings:
New Savings = New Salary - New Expenditure
New Savings = 112−99=13 units.
Calculating Percentage Change in Savings:
Change in Savings = New Savings - Initial Savings = 13−10=3 units.
Percentage Change = (Change / Initial Savings) * 100
Percentage Change = (3/10)×100=30%.
Since the value is positive, it is a 30% increase.
Why the other options are incorrect
- Option (a) - 20% increase: This result would occur if the new savings were 12 units; however, the calculation shows the new savings are 13 units.
- Option (c) - 03% decrease: This is a common error where one might confuse the absolute change (3 units) with a percentage decrease, ignoring that the base value (10) leads to a 30% increase.
- Option (d) - 02% decrease: This might result from incorrectly subtracting the percentage growth of expenditure (10%) from the percentage growth of salary (12%) without accounting for the different base values of salary and expenditure.
Key Concept
The relationship between Salary, Expenditure, and Savings (S=E+Sav) where percentage changes must be applied to their respective absolute base values.