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The income of Raman is ₹12,000. He saves 27% of his income. If his income increases by 20% and expenditure increases by 15%, then his savings will:
decrease by ₹1,089
increase by ₹1,088
increase by ₹1,086
decrease by ₹1,085 Question ID : 441009562158 Option 1 ID : 4410092203902 Option 2 ID : 4410092203901 Option 3 ID : 4410092203899 Option 4 ID : 4410092203900 Status : Answered Chosen Option : C
increase by ₹1,086
Calculate initial savings as 0.27×12000=3240 and expenditure as 0.73×12000=8760. Then apply increases: 1.20×12000 and 1.15×8760, then find the difference.
Initial income = ₹12,000, initial savings = 27% of income, income increase = 20%, expenditure increase = 15%.
Savings=Income−Expenditure
Calculate initial savings as 0.27×12000=3240 and expenditure as 0.73×12000=8760. Then apply increases: 1.20×12000 and 1.15×8760, then find the difference.
Students often calculate the increase in expenditure on the original savings amount rather than the original expenditure amount.
Calculate initial values
Initial income is ₹12,000. Savings are 27% of 12,000, which is 0.27×12000=3240. Thus, initial expenditure is 12000−3240=8760.
Exp1=8760,Sav1=3240
Calculate new values
New income is 12000×1.20=14400. New expenditure is 8760×1.15=10074.
Inc2=14400,Exp2=10074
Calculate new savings and change
New savings is 14400−10074=4326. The change in savings is 4326−3240=1086.
Sav2=4326,ΔSavings=1086
C is correct because the new savings amount is ₹4,326, which represents an increase of ₹1,086 over the initial savings of ₹3,240.
This concept is fundamental to mixture and alligation problems as well as profit and loss equations in financial mathematics.
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