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Mr.John spent 20% of his monthly income on food and 20% on children's education. 40% of the remaining income, he spent on shopping and transport together and 20% of the rest was spent on medical expenses. If he is left with ₹23,040, after all these expenditures, what is his monthly income? 7296
₹86,000
₹96,000
₹80,000
₹92,000
₹80,000
Use the chain multiplier rule: Monthly Income=23040×100−40100×100−40100×100−20100. This avoids calculating each intermediate step individually.
Food and education expense = 20% + 20% = 40% of income. Shopping/transport = 40% of remaining income. Medical = 20% of the next remaining income. Final remaining balance = ₹23,040.
X=(1−a)(1−b)(1−c)Balance
Use the chain multiplier rule: Monthly Income=23040×100−40100×100−40100×100−20100. This avoids calculating each intermediate step individually.
Students often incorrectly sum the percentages (20+20+40+20 = 100%) and assume 0% is left, forgetting that '40% of the remaining' is not the same as 40% of the total income.
Calculate first remaining amount
John spends 20% on food and 20% on education, totaling 40%. The remaining income is 100%−40%=60%.
60% of X=0.6X
Account for shopping and transport
He spends 40% of the remaining 60% on shopping and transport, leaving 60%×(100%−40%)=60%×60%.
0.6X×0.6=0.36X
Account for medical expenses
He spends 20% of the final remainder on medical, leaving 80% of 0.36X.
0.36X×0.8=0.288X
Solve for Income X
Equate the final expression to the balance amount provided: 0.288X=23040. Dividing both sides yields the result.
X=0.28823040=80000
C is correct because calculating the successive remaining balances leads to the equation 0.288X=23040, which gives a monthly income of ₹80,000.
This 'Successive Deduction' method is identical to calculating Compound Depreciation or the 'Population After N years' formula: A=P(1−100r)n.
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