A person earns ₹16,000 per month and spends 80% of his income and saves the remaining amount. If his income increases by 20% and expenditure by 10%, find the percentage of increase in his savings.

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Let's break down the problem step by step:

1. Initial income = ₹16,000
2. Expenditure = 80% of ₹16,000 = (80/100) × 16,000 = ₹12,800
3. Savings = Income - Expenditure = ₹16,000 - ₹12,800 = ₹3,200

Now, income increases by 20%:
New income = ₹16,000 + 20% of ₹16,000 = ₹16,000 + (0.2 × 16,000) = ₹16,000 + ₹3,200 = ₹19,200

Expenditure increases by 10%:
Old expenditure = ₹12,800
New expenditure = ₹12,800 + 10% of ₹12,800 = ₹12,800 + (0.1 × 12,800) = ₹12,800 + ₹1,280 = ₹14,080

New savings = New income - New expenditure = ₹19,200 - ₹14,080 = ₹5,120

Increase in savings = New savings - Old savings = ₹5,120 - ₹3,200 = ₹1,920

Percentage increase in savings = (Increase in savings / Old savings) × 100 = (1,920 / 3,200) × 100 = 0.6 × 100 = 60%

Wait, let's double-check:

Old savings: ₹3,200
New savings: ₹5,120
Increase: ₹1,920
Percentage increase: (1,920 / 3,200) × 100 = 60%

Is the expenditure after increase 80% of new income increased by 10%, or is it 80% of new income, then increased by 10%? The question says 'expenditure by 10%'—so it's 10% more than the original expenditure, not 80% of new income.

So, calculations are correct. The answer is 60%.

Let's check if the expenditure is 80% of new income, then increased by 10% (i.e., 88% of new income):

New expenditure = 80% + 10% of 80% = 88% of new income = 0.88 × 19,200 = ₹16,896
New savings = ₹19,200 - ₹16,896 = ₹2,304
Increase in savings = ₹2,304 - ₹3,200 = -₹896 (a decrease!)

But the question says 'expenditure by 10%'—so it's 10% more than the original expenditure, not 80% of new income.

Therefore, the correct answer is 60%.

So, option 4 is correct. The correct answer is 60%.

Final Answer: 60%

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