Shortcut Trick
Ratio of Savings to Expenditure = (15400 − 7200) : 7200 = 8200 : 7200 = 41 : 36.
Let Savings increase by x%. Total Income ratio = 41 + 36 = 77.
Applying the weighted average principle: (41 × x) + (36 × 5) = 77 × 20
⇒ 41x + 180 = 1540 ⇒ 41x = 1360
⇒ x = 1360 ÷ 41 ≈ 33.17%
∴ The correct answer is 33.17%.
Alternate Method
Income = ₹15,400 (+20% = ₹3,080)
Expenditure
₹7,200
Savings
₹8,200
+5% (₹360)
+33.17% (₹2,720)
Total Increase = 360 + 2720 = ₹3,080
Given:
Initial Income = ₹15,400
Initial Expenditure = ₹7,200
Formula Used:
Savings = Income − Expenditure
Percentage Increase = (Increase in Value ÷ Original Value) × 100
Calculations:
⇒ Initial Savings = 15400 − 7200 = ₹8,200
⇒ New Income = 15400 + (20% of 15400) = 15400 + 3080 = ₹18,480
⇒ New Expenditure = 7200 + (5% of 7200) = 7200 + 360 = ₹7,560
⇒ New Savings = 18480 − 7560 = ₹10,920
⇒ Increase in Savings = 10920 − 8200 = ₹2,720
⇒ Percentage Increase = (2720 ÷ 8200) × 100 = 27200 ÷ 82 ≈ 33.17%
∴ The correct answer is 33.17%.
Additional Information
Income, Expenditure & Savings Relation
The fundamental equation is Income = Expenditure + Savings. Any percentage change in income is mathematically equivalent to the weighted average of the percentage changes in expenditure and savings.
Alligation Method for Percentage Distribution
When a quantity is split into two parts, the net percentage change of the whole is the mean of the percentage changes of the parts. The ratio of the parts is directly proportional to the difference between their individual changes and the overall average change.
Base Value in Percentages
Always calculate the percentage increase or decrease over the original base value. Percentage change = (Final Value − Initial Value) ÷ Initial Value × 100.