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The income of Raman is тВ╣43,800. He saves 20% of his income. If his income increases by 36% and expenditure increases by 40%, then his savings will:
increase by 1,752
decrease by 1,748
increase by 1,757
decrease by 1,753
increase by 1,752
Use 100 as base income: Savings = 20, Expenditure = 80. New Income = 136, New Expenditure = 80 * 1.4 = 112. New Savings = 136 - 112 = 24. Increase is 4 units out of 20 = 20%. Calculate 20% of initial savings.
Initial income is 43,800, savings rate is 20%, income increases by 36%, and expenditure increases by 40%.
Savings=IncomeтИТExpenditure, ╬ФSavings=New┬аSavingsтИТOld┬аSavings
Use 100 as base income: Savings = 20, Expenditure = 80. New Income = 136, New Expenditure = 80 * 1.4 = 112. New Savings = 136 - 112 = 24. Increase is 4 units out of 20 = 20%. Calculate 20% of initial savings.
Students often calculate the percentage increase of the total income rather than the difference in savings directly, or miscalculate the 40% increase on the expenditure value (which is 80% of income, not the full 100%).
Calculate initial values
Initial income is 43,800. Savings are 20% of 43,800, which is 0.20├Ч43800=8760. Expenditure is 43800тИТ8760=35040.
Savings1тАЛ=8760,Exp1тАЛ=35040
Calculate new values
New income is 36% higher: 43800├Ч1.36=59568. New expenditure is 40% higher than original expenditure: 35040├Ч1.40=49056.
Income2тАЛ=59568,Exp2тАЛ=49056
Calculate change in savings
New savings is 59568тИТ49056=10512. The increase is 10512тИТ8760=1752.
╬ФSavings=10512тИТ8760=1752
A is correct because the difference between the new savings of 10,512 and original savings of 8,760 results in an increase of 1,752.
This concept of relative changes in components (income/expenditure/savings) is identical to mixture and allegation problems where the total is divided into two distinct parts.
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