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A man spends 30% of his income on rent and 20% on food. Of the remaining, he spends 50% on miscellaneous items. If he is left with 3,500, what is his monthly income?
10,000
12,000
14,000
16,000
14,000
Use the multiplier method: 3500├Ч100тИТ30тИТ20100тАЛ├Ч100тИТ50100тАЛ. Calculate 3500├Ч2├Ч2=14000.
Rent expenditure = 30%, Food expenditure = 20%, Miscellaneous expenditure on remainder = 50%, Final savings = 3,500.
X=тИП(1тИТ100riтАЛтАЛ)SavingsтАЛ
Use the multiplier method: 3500├Ч100тИТ30тИТ20100тАЛ├Ч100тИТ50100тАЛ. Calculate 3500├Ч2├Ч2=14000.
Students often add 30% + 20% + 50% = 100% and assume he has 0% left, forgetting that the 50% miscellaneous applies only to the remainder.
Calculate total percentage spent before miscellaneous
The man spends 30% on rent and 20% on food, totaling 50%. The remaining income is 100%тИТ50%=50%.
100\% - (30\% + 20\%) = 50\%$$\text{ of total income remains before miscellaneous expenses.}
Account for miscellaneous expenses
He spends 50% of the remaining 50% on miscellaneous items. Thus, he is left with 50% of the remaining 50% income.
50\% \text{ of } 50\% = 0.5 \times 0.5 = 0.25 = 25\%$$\text{ of total income.}
Solve for total income
Given that 25% of the total income is 3,500, we solve for the total income X.
0.25├ЧX=3500тЯ╣X=0.253500тАЛ=14000
C is correct because calculating 25% of 14,000 results in the remaining savings of 3,500.
This concept of 'remaining balance' is frequently applied in Mixture and Alligation problems where ingredients are removed in successive stages.