The ratio of expenditure to savings of a woman is 4 : 1. If her income and expenditure are increased by 20% and 10%, respectively, then find the percentage change in her savings.

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Step 1: Let the savings be S and expenditure be E.  
Given ratio of expenditure to savings = 4 : 1  
So, E = 4x and S = x for some x.

Step 2: Income (I) = Expenditure + Savings = 4x + x = 5x

Step 3: Income is increased by 20%, so new income = 5x * 1.20 = 6x  
Expenditure is increased by 10%, so new expenditure = 4x * 1.10 = 4.4x

Step 4: New savings = New income - New expenditure = 6x - 4.4x = 1.6x

Step 5: Percentage change in savings = ((New savings - Old savings) / Old savings) * 100
= ((1.6x - x) / x) * 100 = (0.6x / x) * 100 = 60%

Hence, the percentage change in savings is 60%.

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