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The expenditure of Swarna is 125% more than her savings. If her expenditure decreases by 6% and savings increases by 26.5%, then by what percentage does her income increase?
20.5%
18.5%
8%
4%
4%
Assume savings = 100, calculate expenditure = 225, income = 325. Apply percentage changes directly to the parts.
Swarna's expenditure is 125% more than her savings. Expenditure decreases by 6%, savings increases by 26.5%.
Income=Expenditure+Savings
Assume savings = 100, calculate expenditure = 225, income = 325. Apply percentage changes directly to the parts.
Confusing '125% more than savings' with '125% of savings'. 125% more means Expenditure = 100% + 125% = 225% of savings.
Step 1: Set up the initial ratio of Savings and Expenditure
Let Swarna's savings be S=100. Since her expenditure is 125% more than her savings, expenditure E=100+125=225.
E=225,S=100
Step 2: Calculate initial Income
Income I is the sum of Expenditure and Savings: I=E+S=225+100=325.
I=225+100=325
Step 3: Calculate the changes in Expenditure and Savings
Expenditure decreases by 6%: ╬ФE=тИТ6%┬аof┬а225=тИТ0.06├Ч225=тИТ13.5. Savings increases by 26.5%: ╬ФS=+26.5%┬аof┬а100=+26.5.
╬ФE=тИТ13.5,╬ФS=+26.5
Step 4: Calculate net change in Income and percentage increase
Net increase in Income ╬ФI=╬ФE+╬ФS=тИТ13.5+26.5=+13. Percentage increase in income = (32513тАЛ)├Ч100=4%.
Percentage┬аIncrease=32513тАЛ├Ч100=4%
D is correct because the calculated percentage increase in Swarna's income is exactly 4%.
Such percentage allocation problems frequently appear in compound mixture and partnership problems in competitive exams.