A mans expenditure and savings are in the ratio of 3:2 his income is increased by 10% expense increased by 12% then the savings increased by what %?

C12

D16

Answer:

In personal finance, the fundamental relationship is Income = Expenditure + Savings. This core formula is crucial for many quantitative aptitude problems.
When a ratio is given, such as Expenditure : Savings = 3 : 2, it's often easiest to assume specific initial values that align with this ratio. For instance, you can assume Expenditure = 3 units and Savings = 2 units.
Therefore, the initial Income would be 3 units + 2 units = 5 units. To make calculations involving percentages simpler, it's advisable to use multiples of 100, such as Expenditure = 300, Savings = 200, and Income = 500. This avoids decimal values in intermediate steps.

Given that income increased by 10%, the new income can be calculated as:
New Income = Initial Income + (Initial Income × Percentage Increase / 100).
Alternatively, a quicker method is: New Income = Initial Income × (1 + Percentage Increase / 100).
Using our assumed values: New Income = 500 × (1 + 10/100) = 500 × 1.10 = 550.

Similarly, expenditure increased by 12%. The new expenditure is calculated as:
New Expenditure = Initial Expenditure × (1 + Percentage Increase / 100).
Using our assumed values: New Expenditure = 300 × (1 + 12/100) = 300 × 1.12 = 336.

Once the new income and new expenditure are known, the new savings can be found using the core formula: New Savings = New Income - New Expenditure.
With our calculated values: New Savings = 550 - 336 = 214.
Now, compare the new savings with the initial savings (200). The increase in savings is 214 - 200 = 14.
To find the percentage increase in savings, use the formula:
Percentage Increase = (Increase in Savings / Initial Savings) × 100%.
Applying the values: Percentage Increase in Savings = (14 / 200) × 100% = 7%.

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